Question is in description

Question

If a is a non-zero, real number and a(x-3)^2-b=c,

•Prove that x=3+or-the square root of b+c/a. Show your work.

•If a=2 and b=5, determine what condition(s) on c will restrict the solutions for x to real numbers.

Explain your reasoning.

PLEASE HELP!

Answer 1

a(x-3)² - b = c

a(x-3)² = b + c

(x-3)² = (b + c)/a

x - 3 = ±√[(b + c)/a]

x = 3 ± √[(b + c)/a]

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If a = 2 and b = 5, then x = 3 ± √[(5 + c)/2]

So, x will be real as long as (5 + c)/2 ≥ 0

5 + c ≥ 0

c ≥ -5