h^2-29h=-36

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Solution for h^2-29h=-36 equation:


Simplifying
h2 + -29h = -36

Reorder the terms:
-29h + h2 = -36

Solving
-29h + h2 = -36

Solving for variable 'h'.

Reorder the terms:
36 + -29h + h2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + -29h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -29h + -36 + h2 = 0 + -36

Reorder the terms:
36 + -36 + -29h + h2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -29h + h2 = 0 + -36
-29h + h2 = 0 + -36

Combine like terms: 0 + -36 = -36
-29h + h2 = -36

The h term is -29h.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29h + 210.25 + h2 = -36 + 210.25

Reorder the terms:
210.25 + -29h + h2 = -36 + 210.25

Combine like terms: -36 + 210.25 = 174.25
210.25 + -29h + h2 = 174.25

Factor a perfect square on the left side:
(h + -14.5)(h + -14.5) = 174.25

Calculate the square root of the right side: 13.200378782

Break this problem into two subproblems by setting 
(h + -14.5) equal to 13.200378782 and -13.200378782.

Subproblem 1

h + -14.5 = 13.200378782 Simplifying h + -14.5 = 13.200378782 Reorder the terms: -14.5 + h = 13.200378782 Solving -14.5 + h = 13.200378782 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + h = 13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + h = 13.200378782 + 14.5 h = 13.200378782 + 14.5 Combine like terms: 13.200378782 + 14.5 = 27.700378782 h = 27.700378782 Simplifying h = 27.700378782

Subproblem 2

h + -14.5 = -13.200378782 Simplifying h + -14.5 = -13.200378782 Reorder the terms: -14.5 + h = -13.200378782 Solving -14.5 + h = -13.200378782 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + h = -13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + h = -13.200378782 + 14.5 h = -13.200378782 + 14.5 Combine like terms: -13.200378782 + 14.5 = 1.299621218 h = 1.299621218 Simplifying h = 1.299621218

Solution

The solution to the problem is based on the solutions from the subproblems. h = {27.700378782, 1.299621218}

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