h(h+4)=15

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Solution for h(h+4)=15 equation:


Simplifying
h(h + 4) = 15

Reorder the terms:
h(4 + h) = 15
(4 * h + h * h) = 15
(4h + h2) = 15

Solving
4h + h2 = 15

Solving for variable 'h'.

Reorder the terms:
-15 + 4h + h2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 4h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 4h + 15 + h2 = 0 + 15

Reorder the terms:
-15 + 15 + 4h + h2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 4h + h2 = 0 + 15
4h + h2 = 0 + 15

Combine like terms: 0 + 15 = 15
4h + h2 = 15

The h term is 4h.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4h + 4 + h2 = 15 + 4

Reorder the terms:
4 + 4h + h2 = 15 + 4

Combine like terms: 15 + 4 = 19
4 + 4h + h2 = 19

Factor a perfect square on the left side:
(h + 2)(h + 2) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(h + 2) equal to 4.358898944 and -4.358898944.

Subproblem 1

h + 2 = 4.358898944 Simplifying h + 2 = 4.358898944 Reorder the terms: 2 + h = 4.358898944 Solving 2 + h = 4.358898944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + h = 4.358898944 + -2 h = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 h = 2.358898944 Simplifying h = 2.358898944

Subproblem 2

h + 2 = -4.358898944 Simplifying h + 2 = -4.358898944 Reorder the terms: 2 + h = -4.358898944 Solving 2 + h = -4.358898944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + h = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + h = -4.358898944 + -2 h = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 h = -6.358898944 Simplifying h = -6.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. h = {2.358898944, -6.358898944}

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