Question

Please help me 15 point

Answer 1

`(x + 8)^2 = 55`

Explanation:

Given

`x^2 + 16x + 17 = 8`

Required

Get an equivalent equation

`x^2 + 16x + 17 = 8`

Subtract 17 from both sides

`x^2 + 16x + 17-17 = 8-17`

`x^2 + 16x = -9`

Add 64 to both sides

`x^2 + 16x + 64 = -9+64`

`x^2 + 16x + 64 = 55`

Expand the expression on the left-hand side

`x^2 + 8x + 8x + 64 = 55`

Factorize:

`x(x + 8) + 8(x + 8)= 55`

`(x + 8)(x + 8)= 55`

`(x + 8)^2 = 55`