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Maths-

General

Easy

Question

What is the solution to the equation $open parentheses x squared plus 5 x plus 25 close parentheses to the power of 3 over 2 end exponent equals 343$

hint Hint:

Rearrange the equation and then solve for .

The correct answer is: x = 3, - 8

Complete step by step solution:
Here we have the equation $open parentheses x squared plus 5 x plus 25 close parentheses to the power of 3 over 2 end exponent equals 343$
To make the power of the equation as 1, we have to raise the equation by $2 over 3$
$not stretchy rightwards double arrow open parentheses x squared plus 5 x plus 25 close parentheses to the power of 3 over 2 cross times 2 over 3 end exponent equals 343 to the power of 2 over 3 end exponent$
$not stretchy rightwards double arrow open parentheses x squared plus 5 x plus 25 close parentheses equals cube root of 343 squared end root$
$not stretchy rightwards double arrow x squared plus 5 x plus 25 equals 49$
On rearranging, we have $x squared plus 5 x minus 24 equals 0$
Now, this is a quadratic equation with a = 1, b = 5, c = -24
Roots can be found with, $x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
$x equals fraction numerator negative 5 plus-or-minus square root of 25 minus 4 cross times 1 cross times negative 24 end root over denominator 2 cross times 1 end fraction$
On solving, we get x = 3, - 8

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