Question
What is one possible solution to the equation above?
Hint:
Hint:
We are given an equation in one variable. To find one solution of the equation means to find a value of x which satisfies this equation. First we expand the square in the left and side and then simplify the equation. We need to use this formula to expand the square term
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We may also need to use the quadratic formula, which is
The correct answer is: 2 or 3
The given equation is
Expanding the square terms by the formula
We get,
Taking all the terms to the left hand side, we have
Taking the co-efficient common which have the same power of x with them,
Simplifying, we get,
This is a quadratic equation of the form 
The value of x is given by
Comparing the above equation with the quadratic equation, we have
So the value of x is given by
Thus, we get
Thus, we get two values of x
By taking the ‘+’ sign, we have
By taking the ‘-‘ sign, we get
Hence, value of x = 2 or 3
One possible solution to the equation 
or
One possible solution to the equation 
Note:
Instead of using the quadratic formula, we could also use middle term factorization to solve the quadratic equation
in the following way:
Thus we get values of x = 2 or 3 .
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△ ABC ≅△ PQR
AB = 10 ft, BC = 6 ft, AC = 6 ft
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Find the values of x and y.
△ ABC ≅△ PQR
AB = 10 ft, BC = 6 ft, AC = 6 ft
PQ = 2y, QR = x + 2, RS = 2x − 2
Find the values of x and y.
In the equation above, what is the value of s when t= -1 ?
Note:
Instead of adding 1 on both sides, we can also understand the concept by taking _1 of the left hand side on the right hand side and then the sign changes to +1 . Similarly, instead of dividing by 2, we can understand it by saying that we take 2 from the left hand side to the right hand side, and here it becomes division.
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
In the equation above, what is the value of s when t= -1 ?
Note:
Instead of adding 1 on both sides, we can also understand the concept by taking _1 of the left hand side on the right hand side and then the sign changes to +1 . Similarly, instead of dividing by 2, we can understand it by saying that we take 2 from the left hand side to the right hand side, and here it becomes division.
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
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Note:
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Which of the following is an equivalent form of the expression?
Note:
Another way to solve this problem is to expand or simplify the expression given in the question. Then we expand the expressions given in the options and check which one of them is equal to the one given in question.
We need to be careful while simplifying the expressions
