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

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)

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