h^2+26h-10=0

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Solution for h^2+26h-10=0 equation:


Simplifying
h2 + 26h + -10 = 0

Reorder the terms:
-10 + 26h + h2 = 0

Solving
-10 + 26h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 26h + 10 + h2 = 0 + 10

Reorder the terms:
-10 + 10 + 26h + h2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 26h + h2 = 0 + 10
26h + h2 = 0 + 10

Combine like terms: 0 + 10 = 10
26h + h2 = 10

The h term is 26h.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26h + 169 + h2 = 10 + 169

Reorder the terms:
169 + 26h + h2 = 10 + 169

Combine like terms: 10 + 169 = 179
169 + 26h + h2 = 179

Factor a perfect square on the left side:
(h + 13)(h + 13) = 179

Calculate the square root of the right side: 13.37908816

Break this problem into two subproblems by setting 
(h + 13) equal to 13.37908816 and -13.37908816.

Subproblem 1

h + 13 = 13.37908816 Simplifying h + 13 = 13.37908816 Reorder the terms: 13 + h = 13.37908816 Solving 13 + h = 13.37908816 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + h = 13.37908816 + -13 Combine like terms: 13 + -13 = 0 0 + h = 13.37908816 + -13 h = 13.37908816 + -13 Combine like terms: 13.37908816 + -13 = 0.37908816 h = 0.37908816 Simplifying h = 0.37908816

Subproblem 2

h + 13 = -13.37908816 Simplifying h + 13 = -13.37908816 Reorder the terms: 13 + h = -13.37908816 Solving 13 + h = -13.37908816 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + h = -13.37908816 + -13 Combine like terms: 13 + -13 = 0 0 + h = -13.37908816 + -13 h = -13.37908816 + -13 Combine like terms: -13.37908816 + -13 = -26.37908816 h = -26.37908816 Simplifying h = -26.37908816

Solution

The solution to the problem is based on the solutions from the subproblems. h = {0.37908816, -26.37908816}

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