h^2+16h-128=0

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Solution for h^2+16h-128=0 equation:


Simplifying
h2 + 16h + -128 = 0

Reorder the terms:
-128 + 16h + h2 = 0

Solving
-128 + 16h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 16h + 128 + h2 = 0 + 128

Reorder the terms:
-128 + 128 + 16h + h2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 16h + h2 = 0 + 128
16h + h2 = 0 + 128

Combine like terms: 0 + 128 = 128
16h + h2 = 128

The h term is 16h.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16h + 64 + h2 = 128 + 64

Reorder the terms:
64 + 16h + h2 = 128 + 64

Combine like terms: 128 + 64 = 192
64 + 16h + h2 = 192

Factor a perfect square on the left side:
(h + 8)(h + 8) = 192

Calculate the square root of the right side: 13.856406461

Break this problem into two subproblems by setting 
(h + 8) equal to 13.856406461 and -13.856406461.

Subproblem 1

h + 8 = 13.856406461 Simplifying h + 8 = 13.856406461 Reorder the terms: 8 + h = 13.856406461 Solving 8 + h = 13.856406461 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + h = 13.856406461 + -8 Combine like terms: 8 + -8 = 0 0 + h = 13.856406461 + -8 h = 13.856406461 + -8 Combine like terms: 13.856406461 + -8 = 5.856406461 h = 5.856406461 Simplifying h = 5.856406461

Subproblem 2

h + 8 = -13.856406461 Simplifying h + 8 = -13.856406461 Reorder the terms: 8 + h = -13.856406461 Solving 8 + h = -13.856406461 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + h = -13.856406461 + -8 Combine like terms: 8 + -8 = 0 0 + h = -13.856406461 + -8 h = -13.856406461 + -8 Combine like terms: -13.856406461 + -8 = -21.856406461 h = -21.856406461 Simplifying h = -21.856406461

Solution

The solution to the problem is based on the solutions from the subproblems. h = {5.856406461, -21.856406461}

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