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

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

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)