Answer:
x = +[tex]\sqrt{71} - 8[/tex] , -[tex]\sqrt{71} - 8[/tex]
x ≈ .426, -16.426
Step-by-step explanation:
When we complete the square, we add a value to both sides to make the left side a "perfect square" that we can simplify to (a+b)^2.
x^2 + 16x = 7
x^2 + 16x + _____ = 7 + ______
What do we put in the blank? The formula is to take half of b, then square that. Half of 16 is 8, 8^2 is 64, so
x^2 + 16x + 64 = 7 + 64
Now on the left side we have a perfect square!
(x+8)^2 = 71
Now all that's left to do is simplify this to get x. First take the square root of both sides.
x+8 = [tex]\sqrt{71}[/tex]
x = +[tex]\sqrt{71} - 8[/tex] , -[tex]\sqrt{71} - 8[/tex]
x ≈ .426, -16.426
