Question

Solve the equation by completing the square. x2 + 16x = 7

Answer 1

x = +
`√(71) - 8` , -
`√(71) - 8`

x ≈ .426, -16.426

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 =
`√(71)`

x = +
`√(71) - 8` , -
`√(71) - 8`

x ≈ .426, -16.426