h^2+15h-90=0

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Solution for h^2+15h-90=0 equation:


Simplifying
h2 + 15h + -90 = 0

Reorder the terms:
-90 + 15h + h2 = 0

Solving
-90 + 15h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 15h + 90 + h2 = 0 + 90

Reorder the terms:
-90 + 90 + 15h + h2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 15h + h2 = 0 + 90
15h + h2 = 0 + 90

Combine like terms: 0 + 90 = 90
15h + h2 = 90

The h term is 15h.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15h + 56.25 + h2 = 90 + 56.25

Reorder the terms:
56.25 + 15h + h2 = 90 + 56.25

Combine like terms: 90 + 56.25 = 146.25
56.25 + 15h + h2 = 146.25

Factor a perfect square on the left side:
(h + 7.5)(h + 7.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(h + 7.5) equal to 12.093386622 and -12.093386622.

Subproblem 1

h + 7.5 = 12.093386622 Simplifying h + 7.5 = 12.093386622 Reorder the terms: 7.5 + h = 12.093386622 Solving 7.5 + h = 12.093386622 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + h = 12.093386622 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + h = 12.093386622 + -7.5 h = 12.093386622 + -7.5 Combine like terms: 12.093386622 + -7.5 = 4.593386622 h = 4.593386622 Simplifying h = 4.593386622

Subproblem 2

h + 7.5 = -12.093386622 Simplifying h + 7.5 = -12.093386622 Reorder the terms: 7.5 + h = -12.093386622 Solving 7.5 + h = -12.093386622 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + h = -12.093386622 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + h = -12.093386622 + -7.5 h = -12.093386622 + -7.5 Combine like terms: -12.093386622 + -7.5 = -19.593386622 h = -19.593386622 Simplifying h = -19.593386622

Solution

The solution to the problem is based on the solutions from the subproblems. h = {4.593386622, -19.593386622}

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