.5(h+5)(h)=18

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Solution for .5(h+5)(h)=18 equation:


Simplifying
0.5(h + 5)(h) = 18

Reorder the terms:
0.5(5 + h)(h) = 18

Reorder the terms for easier multiplication:
0.5h(5 + h) = 18
(5 * 0.5h + h * 0.5h) = 18
(2.5h + 0.5h2) = 18

Solving
2.5h + 0.5h2 = 18

Solving for variable 'h'.

Reorder the terms:
-18 + 2.5h + 0.5h2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 2.5h + 0.5h2 = 0

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-36 + 5h + h2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 5h + 36 + h2 = 0 + 36

Reorder the terms:
-36 + 36 + 5h + h2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 5h + h2 = 0 + 36
5h + h2 = 0 + 36

Combine like terms: 0 + 36 = 36
5h + h2 = 36

The h term is 5h.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5h + 6.25 + h2 = 36 + 6.25

Reorder the terms:
6.25 + 5h + h2 = 36 + 6.25

Combine like terms: 36 + 6.25 = 42.25
6.25 + 5h + h2 = 42.25

Factor a perfect square on the left side:
(h + 2.5)(h + 2.5) = 42.25

Calculate the square root of the right side: 6.5

Break this problem into two subproblems by setting 
(h + 2.5) equal to 6.5 and -6.5.

Subproblem 1

h + 2.5 = 6.5 Simplifying h + 2.5 = 6.5 Reorder the terms: 2.5 + h = 6.5 Solving 2.5 + h = 6.5 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + h = 6.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = 6.5 + -2.5 h = 6.5 + -2.5 Combine like terms: 6.5 + -2.5 = 4 h = 4 Simplifying h = 4

Subproblem 2

h + 2.5 = -6.5 Simplifying h + 2.5 = -6.5 Reorder the terms: 2.5 + h = -6.5 Solving 2.5 + h = -6.5 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + h = -6.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = -6.5 + -2.5 h = -6.5 + -2.5 Combine like terms: -6.5 + -2.5 = -9 h = -9 Simplifying h = -9

Solution

The solution to the problem is based on the solutions from the subproblems. h = {4, -9}

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