Question

h^2+14h=-31 Solve by completing the square

write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth

Answer 1

Since the constant has been moved to the left side, you can move on to the next step which is adding (b/2)² to both sides of the equation.

h² + 14h + (14/2)² = -31 + (14/2)²

Simplify the parenthesis and exponent.

h² + 14h + 7² = -31 + 7²

h² + 14h + 49 = -31 + 49

h² + 14h + 49 = 18

Factor the expression of the left.

(h + 7)(h + 7) = 18

Take the square root of both sides.

√(h + 7)(h + 7) = ± √9 • 2

(h + 7) = ± 3√2

h + 7 = ± 3√2

Subtract 7 from both sides.

You solutions are:

h = -7 + 3√2 → -2.7573 → -2.76

h = -7 - 3√2 → -11.2426 → -11.24

Answer 2

Given   H^2+14h=-31, let's complete the square of the 1st two terms:

h^2 + 14h + (14/2)^2  =  -31 + (14/2)^2

  h^2 + 14h + 49   =   -31 + 49 = 18

   (h+7)^2 = 18

Taking the sqrt of both sides,

h+7 = sqrt (9*2) = 3 sqrt(2)

Solving for h,    h= -7 plus or minus 3 sqrt(2)    (answer)