2h^2-h-12=0

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Solution for 2h^2-h-12=0 equation:


Simplifying
2h2 + -1h + -12 = 0

Reorder the terms:
-12 + -1h + 2h2 = 0

Solving
-12 + -1h + 2h2 = 0

Solving for variable 'h'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-6 + -0.5h + h2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -0.5h + 6 + h2 = 0 + 6

Reorder the terms:
-6 + 6 + -0.5h + h2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -0.5h + h2 = 0 + 6
-0.5h + h2 = 0 + 6

Combine like terms: 0 + 6 = 6
-0.5h + h2 = 6

The h term is -0.5h.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5h + 0.0625 + h2 = 6 + 0.0625

Reorder the terms:
0.0625 + -0.5h + h2 = 6 + 0.0625

Combine like terms: 6 + 0.0625 = 6.0625
0.0625 + -0.5h + h2 = 6.0625

Factor a perfect square on the left side:
(h + -0.25)(h + -0.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(h + -0.25) equal to 2.46221445 and -2.46221445.

Subproblem 1

h + -0.25 = 2.46221445 Simplifying h + -0.25 = 2.46221445 Reorder the terms: -0.25 + h = 2.46221445 Solving -0.25 + h = 2.46221445 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + h = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + h = 2.46221445 + 0.25 h = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 h = 2.71221445 Simplifying h = 2.71221445

Subproblem 2

h + -0.25 = -2.46221445 Simplifying h + -0.25 = -2.46221445 Reorder the terms: -0.25 + h = -2.46221445 Solving -0.25 + h = -2.46221445 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + h = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + h = -2.46221445 + 0.25 h = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 h = -2.21221445 Simplifying h = -2.21221445

Solution

The solution to the problem is based on the solutions from the subproblems. h = {2.71221445, -2.21221445}

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