h^2-25h=100

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Solution for h^2-25h=100 equation:


Simplifying
h2 + -25h = 100

Reorder the terms:
-25h + h2 = 100

Solving
-25h + h2 = 100

Solving for variable 'h'.

Reorder the terms:
-100 + -25h + h2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -25h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -25h + 100 + h2 = 0 + 100

Reorder the terms:
-100 + 100 + -25h + h2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -25h + h2 = 0 + 100
-25h + h2 = 0 + 100

Combine like terms: 0 + 100 = 100
-25h + h2 = 100

The h term is -25h.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25h + 156.25 + h2 = 100 + 156.25

Reorder the terms:
156.25 + -25h + h2 = 100 + 156.25

Combine like terms: 100 + 156.25 = 256.25
156.25 + -25h + h2 = 256.25

Factor a perfect square on the left side:
(h + -12.5)(h + -12.5) = 256.25

Calculate the square root of the right side: 16.007810594

Break this problem into two subproblems by setting 
(h + -12.5) equal to 16.007810594 and -16.007810594.

Subproblem 1

h + -12.5 = 16.007810594 Simplifying h + -12.5 = 16.007810594 Reorder the terms: -12.5 + h = 16.007810594 Solving -12.5 + h = 16.007810594 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + h = 16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + h = 16.007810594 + 12.5 h = 16.007810594 + 12.5 Combine like terms: 16.007810594 + 12.5 = 28.507810594 h = 28.507810594 Simplifying h = 28.507810594

Subproblem 2

h + -12.5 = -16.007810594 Simplifying h + -12.5 = -16.007810594 Reorder the terms: -12.5 + h = -16.007810594 Solving -12.5 + h = -16.007810594 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + h = -16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + h = -16.007810594 + 12.5 h = -16.007810594 + 12.5 Combine like terms: -16.007810594 + 12.5 = -3.507810594 h = -3.507810594 Simplifying h = -3.507810594

Solution

The solution to the problem is based on the solutions from the subproblems. h = {28.507810594, -3.507810594}

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