1. Explain why the equation (x-4) ^2 - 28=8 has two solutions. Then solve the equation to find the solutions. Show your work.

(x-4) ^2 extended is x^2 - 8x + 16. Then you substitute that in and you get x^2 - 8x + 16 - 28 = 8. 16-28 = - 12. Then you subtract 8 on both sides. You get x^2 - 8x - 12 - 8 = 0. - 12-8=-20. x^2 - 8x - 20 = 0. Then you use the quadratic formula and you get the 2 answers.

The equation is a second degree equation so it will have 2 solutions.

Theeasiest way To solve this equation is the 'square root method'.

First I'll get the 'square on the left and everything else on the right.

(x - 4) ^2 - 28 = 8

Add 28 to both sides.

(x - 4) ^2 = 36

Take the square root of both sides

x - 4 = + - 6

Add 4 to both sides.

x = 4 + - 6

x = 4 + 6 = 10

x = 4 - 6 = - 2