Question

How do you solve for x?

2(x - 3)^2 - 32 = 0

Answer 1

$\: \: \: \: \: \: \: \:$

$x = - 1 \\ x = \: 7$

Step-by-step explanation:

$2(x - 3 {)}^{2} - 32 = 0$

• divide both sides

$(x - 3 {)}^{2} - 16 = 0$

• use a²- b² =(a - b ) (a + b) to factor the expression

$(x - 3 - 4) \times (x - 3 + 4) = 0$

• calculate the difference and the sum

$(x - 7) \times (x + 1) = 0$

• when the product of factors equals 0 ,at least one factor is 0

$x - 7 = 0 \\ x + 1 = 0$

• solve the equation for x

$x = 7 \\ x + 1 = 0$

• the equation has 2 solutions

$x = - 1 \\ x = 7$

hope it helps

$\: \: \: \: \: \: \:$