Question

2(x-1)^2 +7= 39 helppp

Answer 1

x = 5 or x = -3

Explanation:

We know that,

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

Accordingly, let us solve this.

2 ( x - 1 )² + 7 = 39

First, solve the brackets.

2 ( x² - 2x + 1 ) + 7 = 39

2x² - 4x + 2 + 7 = 39

Subtract 39 from both sides.

2x² - 4x - 30 = 0

Divide the whole equation by 2.

x² - 2x - 15 = 0

Solve the quadratic equation.

x² + 3x - 5x - 15 = 0

x ( x + 3 ) - 5 ( x + 3 ) = 0

( x - 5 ) ( x + 3 ) = 0

∴ x - 5 = 0 x + 3 = 0

x = 5 or x = -3

Answer 2

x = 5 or x = -3

Explanation:

2(x-1)^2 +7= 39

Subtract 7 from each side.

2(x-1)^2 +7-7= 39 -7

2(x-1)^2 = 32

Divide each side by 2.

2/2(x-1)^2 = 32/2

(x-1)^2 = 16

Take the square root of each side.

sqrt((x-1)^2)= sqrt(16)

x-1 = ±4

Add 1 to each side.

x = ±4 +1

x = 5 or x = -3