h^2-6h=31

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Solution for h^2-6h=31 equation:


Simplifying
h2 + -6h = 31

Reorder the terms:
-6h + h2 = 31

Solving
-6h + h2 = 31

Solving for variable 'h'.

Reorder the terms:
-31 + -6h + h2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + -6h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -6h + 31 + h2 = 0 + 31

Reorder the terms:
-31 + 31 + -6h + h2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -6h + h2 = 0 + 31
-6h + h2 = 0 + 31

Combine like terms: 0 + 31 = 31
-6h + h2 = 31

The h term is -6h.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6h + 9 + h2 = 31 + 9

Reorder the terms:
9 + -6h + h2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + -6h + h2 = 40

Factor a perfect square on the left side:
(h + -3)(h + -3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(h + -3) equal to 6.32455532 and -6.32455532.

Subproblem 1

h + -3 = 6.32455532 Simplifying h + -3 = 6.32455532 Reorder the terms: -3 + h = 6.32455532 Solving -3 + h = 6.32455532 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + h = 6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + h = 6.32455532 + 3 h = 6.32455532 + 3 Combine like terms: 6.32455532 + 3 = 9.32455532 h = 9.32455532 Simplifying h = 9.32455532

Subproblem 2

h + -3 = -6.32455532 Simplifying h + -3 = -6.32455532 Reorder the terms: -3 + h = -6.32455532 Solving -3 + h = -6.32455532 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + h = -6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + h = -6.32455532 + 3 h = -6.32455532 + 3 Combine like terms: -6.32455532 + 3 = -3.32455532 h = -3.32455532 Simplifying h = -3.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. h = {9.32455532, -3.32455532}

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