Maths-
General
Easy

Question

Solve 2 open parentheses x squared minus 12 x minus 4 close parentheses to the power of 1 half end exponent minus 3 equals 15

hintHint:

Rearrange the equation and then solve.

The correct answer is: x = 17, - 5


    Complete step by step solution:
    Here we have the equation 2 open parentheses x squared minus 12 x minus 4 close parentheses to the power of 1 half end exponent minus 3 equals 15
    On adding 3 on both the sides, we get 2 open parentheses x squared minus 12 x minus 4 close parentheses to the power of 1 half end exponent equals 18
    On dividing both the sides by 2, we get open parentheses x squared minus 12 x minus 4 close parentheses to the power of 1 half end exponent equals 9
    To make the power of the equation as 1, we have to raise the equation by 2

    not stretchy rightwards double arrow open parentheses x squared minus 12 x minus 4 close parentheses to the power of 1 half cross times 2 end exponent equals 9 squared

    not stretchy rightwards double arrow x squared minus 12 x minus 4 equals 81
    On rearranging, we get x squared minus 12 x minus 85 equals 0
    Now, this is a quadratic equation with a = 1, b = - 12, c = - 85
    Roots can be found with, x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    x equals fraction numerator 12 plus-or-minus square root of 144 minus 4 cross times 1 cross times negative 85 end root over denominator 2 cross times 1 end fraction
    On solving, we get x = 17, - 5

    Related Questions to study

    General
    Maths-

    Solve the radical equation square root of x minus 2 end root plus 3 equals 5

    Solve the radical equation square root of x minus 2 end root plus 3 equals 5

    Maths-General
    General
    Maths-

    Solve 5x - 48 = -3x + 8

    Solve 5x - 48 = -3x + 8

    Maths-General
    General
    Maths-

    Solve the radical equation ∛x + 2 = 4

    Solve the radical equation ∛x + 2 = 4

    Maths-General
    parallel
    General
    Maths-

    Aaron can join a gym that charges $19.99 per month plus an annual $12.80 fee , or he can pay $21.59 per month. he thinks the second option is better because he plans to use the gym for 10 months. Is Aaron correct ? Explain.

    Aaron can join a gym that charges $19.99 per month plus an annual $12.80 fee , or he can pay $21.59 per month. he thinks the second option is better because he plans to use the gym for 10 months. Is Aaron correct ? Explain.

    Maths-General
    General
    Maths-

    How can you determine whether the data in the table can be modelled by a quadratic function ?

    How can you determine whether the data in the table can be modelled by a quadratic function ?

    Maths-General
    General
    Maths-

    A red balloon is 40 feet above the ground and rising at 2ft/s . At the same time , a blue balloon is at 60 feet above the ground and descending at 3 ft/s , What will the height of the balloon be when they are the same height above the ground ?

    A red balloon is 40 feet above the ground and rising at 2ft/s . At the same time , a blue balloon is at 60 feet above the ground and descending at 3 ft/s , What will the height of the balloon be when they are the same height above the ground ?

    Maths-General
    parallel
    General
    Maths-

    Solve the radical equation x equals square root of 56 minus x end root  Check for extraneous solutions

    Solve the radical equation x equals square root of 56 minus x end root  Check for extraneous solutions

    Maths-General
    General
    Maths-

    Solve 34-2x= 7x

    Solve 34-2x= 7x

    Maths-General
    General
    Maths-

    How can you determine whether the data in the table can be modelled by a linear function ?

    How can you determine whether the data in the table can be modelled by a linear function ?

    Maths-General
    parallel
    General
    Maths-

    Solve the radical equation square root of x plus 5 end root minus 1 equals 3
     

    Solve the radical equation square root of x plus 5 end root minus 1 equals 3
     

    Maths-General
    General
    Maths-

    Solve 27-3X= 3X+27

    Solve 27-3X= 3X+27

    Maths-General
    General
    Maths-

    two year prepaid membership at gym A costs $250 for the first year plus $19 per month for the second year . A two year prepaid membership at Gym B costs $195 for the first year plus $24 per month for the second year , Leah says the cost for both gym memberships will be the same after the 11th month of the second year , Do you agree , Explain.

    A second-degree quadratic equation is an algebraic equation in x. Ax² + bx + c = 0, where 'x' is the variable, 'a' and 'b' are the coefficients, and 'c' is the constant term, is the quadratic equation in its standard form. A non-zero term (a ≠ 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation. The x² term is written first, then the x term, and finally, the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of a, b, and c are not expressed as decimals or fractions but are written as integral values. There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are referred to as the quadratic equations' roots and are given the designations (α, β). There are several ways to present the quadratic equations: (x - 1)(x + 2) = 0, 5x(x + 3) = 12x, x³ = x(x² + x - 3), where -x²= -3x + 1. Before carrying out any additional procedures, these equations are to be translated into the quadratic equation's standard form.

    two year prepaid membership at gym A costs $250 for the first year plus $19 per month for the second year . A two year prepaid membership at Gym B costs $195 for the first year plus $24 per month for the second year , Leah says the cost for both gym memberships will be the same after the 11th month of the second year , Do you agree , Explain.

    Maths-General

    A second-degree quadratic equation is an algebraic equation in x. Ax² + bx + c = 0, where 'x' is the variable, 'a' and 'b' are the coefficients, and 'c' is the constant term, is the quadratic equation in its standard form. A non-zero term (a ≠ 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation. The x² term is written first, then the x term, and finally, the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of a, b, and c are not expressed as decimals or fractions but are written as integral values. There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are referred to as the quadratic equations' roots and are given the designations (α, β). There are several ways to present the quadratic equations: (x - 1)(x + 2) = 0, 5x(x + 3) = 12x, x³ = x(x² + x - 3), where -x²= -3x + 1. Before carrying out any additional procedures, these equations are to be translated into the quadratic equation's standard form.

    parallel
    General
    Maths-

    Solve the radical equation 4 x equals square root of 6 x plus 10 end root. Check for extraneous solutions

    Solve the radical equation 4 x equals square root of 6 x plus 10 end root. Check for extraneous solutions

    Maths-General
    General
    Maths-

    Solve : 7X= 8X+12

    Solve : 7X= 8X+12

    Maths-General
    General
    Maths-

    Determine whether a table shows a linear , quadratic or exponential function ?

    Determine whether a table shows a linear , quadratic or exponential function ?

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.