h^2-h-22=0

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Solution for h^2-h-22=0 equation:


Simplifying
h2 + -1h + -22 = 0

Reorder the terms:
-22 + -1h + h2 = 0

Solving
-22 + -1h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -1h + 22 + h2 = 0 + 22

Reorder the terms:
-22 + 22 + -1h + h2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1h + h2 = 0 + 22
-1h + h2 = 0 + 22

Combine like terms: 0 + 22 = 22
-1h + h2 = 22

The h term is -1h.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1h + 0.25 + h2 = 22 + 0.25

Reorder the terms:
0.25 + -1h + h2 = 22 + 0.25

Combine like terms: 22 + 0.25 = 22.25
0.25 + -1h + h2 = 22.25

Factor a perfect square on the left side:
(h + -0.5)(h + -0.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(h + -0.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

h + -0.5 = 4.716990566 Simplifying h + -0.5 = 4.716990566 Reorder the terms: -0.5 + h = 4.716990566 Solving -0.5 + h = 4.716990566 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + h = 4.716990566 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + h = 4.716990566 + 0.5 h = 4.716990566 + 0.5 Combine like terms: 4.716990566 + 0.5 = 5.216990566 h = 5.216990566 Simplifying h = 5.216990566

Subproblem 2

h + -0.5 = -4.716990566 Simplifying h + -0.5 = -4.716990566 Reorder the terms: -0.5 + h = -4.716990566 Solving -0.5 + h = -4.716990566 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + h = -4.716990566 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + h = -4.716990566 + 0.5 h = -4.716990566 + 0.5 Combine like terms: -4.716990566 + 0.5 = -4.216990566 h = -4.216990566 Simplifying h = -4.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. h = {5.216990566, -4.216990566}

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