Question

30 points for full answer.

1. Solve the equation: (x-4)^2-28=8

Show your work. Don’t forget that you will get two answers. Use the square root property to solve

2. This is Josh’s solution for the equation :
Step 1: x² - 6x – 7 = 0
Step 2: x² - 6x = 7
Step 3: x² - 6x + 9 = 7 + 9
Step 4: (x – 3)² = 16
Step 5: x – 3 = 16
Step 6: x = 19
Step 7: x – 3 = -16
Step 8: x = -13

Where did Josh make his mistake? What are the solutions to this equation? Show all of your work. This problem is solved using completing the square.

The mistake was in step _____________. Here is how to correctly solve the equation:

Answer 1

Josh made his mistae in Step 5! Hope this helps with one!

Answer 2

1. (x-4)^2-28 = 8
(x-4)^2 = 36, we square both sides and get;
x-4 = 6, x = 10
and
x-4 = -6, x = -2
2. The mistake was in step 5.
x² - 6x – 7 = 0; x² - 6x = 7; x² - 6x + 9 = 7 + 9; (x – 3)² = 16
x – 3 = 4; x = 7
x – 3 = -4; x = -1
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Hope this helps!