Please help me Use (x − 4)^2 − 28 = 8 for the following:

a. Explain why (x − 4)^2 − 28 = 8 has two solutions. (5 pts)

b. Solve the equation to find the solutions. Show your work. (5 pts)

a) Because both sides are perfect squares b) (x-4)² – 28 = 8

(x–4)² = 36

Square root both sides

√(x–4)² = √36

x–4 = 6

x= 10

Step-by-step explanation:

(x–4)(x–4) = 36

x² – 8x+ 16 = 36

x² – 8x – 20 = 0

(x² + 2x)( –10x – 20) = 0

x(x+2) – 10(x+2) = 0

(x+2)(x–10) = 0

x = 10 or –2

x = 10

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