Answer:
Factored equation: (x-4)² = 55
Solution set
x = 11.416 and x = -3.416
Explanation:
Given equation is
x² - 8x = 39
We have to somehow get this equation in the form (x + a)² = b
(x + a)² = x² +2ax + a²
Comparing we get
2ax = -8x
==> a = -4
Add a² = (-4)² = 16 to both sides of x² - 8x = 39
==> x² - 8x +16 = 39 + 16
==> x² - 8x +16 = 55
x² - 8x + 16 = (x - 4)²
==> (x-4)² = 55
I think this is what they were asking, not exactly the solution to the original equation.
Nevertheless,
(x-4)² = 55
==> x - 4 = ±√55
==> x = 4 ± √55
==> x = 4 + √55 and x = 4 - √55 are the two roots
This works out to
x = 11.416 and x = -3.416