2h(6h-5)=-1

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Solution for 2h(6h-5)=-1 equation:


Simplifying
2h(6h + -5) = -1

Reorder the terms:
2h(-5 + 6h) = -1
(-5 * 2h + 6h * 2h) = -1
(-10h + 12h2) = -1

Solving
-10h + 12h2 = -1

Solving for variable 'h'.

Reorder the terms:
1 + -10h + 12h2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -10h + 12h2 = 0

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

Divide each side by '12'.
0.08333333333 + -0.8333333333h + h2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + -0.8333333333h + -0.08333333333 + h2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + -0.8333333333h + h2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + -0.8333333333h + h2 = 0 + -0.08333333333
-0.8333333333h + h2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
-0.8333333333h + h2 = -0.08333333333

The h term is -0.8333333333h.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333h + 0.1736111111 + h2 = -0.08333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333h + h2 = -0.08333333333 + 0.1736111111

Combine like terms: -0.08333333333 + 0.1736111111 = 0.09027777777
0.1736111111 + -0.8333333333h + h2 = 0.09027777777

Factor a perfect square on the left side:
(h + -0.4166666667)(h + -0.4166666667) = 0.09027777777

Calculate the square root of the right side: 0.300462606

Break this problem into two subproblems by setting 
(h + -0.4166666667) equal to 0.300462606 and -0.300462606.

Subproblem 1

h + -0.4166666667 = 0.300462606 Simplifying h + -0.4166666667 = 0.300462606 Reorder the terms: -0.4166666667 + h = 0.300462606 Solving -0.4166666667 + h = 0.300462606 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + h = 0.300462606 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + h = 0.300462606 + 0.4166666667 h = 0.300462606 + 0.4166666667 Combine like terms: 0.300462606 + 0.4166666667 = 0.7171292727 h = 0.7171292727 Simplifying h = 0.7171292727

Subproblem 2

h + -0.4166666667 = -0.300462606 Simplifying h + -0.4166666667 = -0.300462606 Reorder the terms: -0.4166666667 + h = -0.300462606 Solving -0.4166666667 + h = -0.300462606 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + h = -0.300462606 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + h = -0.300462606 + 0.4166666667 h = -0.300462606 + 0.4166666667 Combine like terms: -0.300462606 + 0.4166666667 = 0.1162040607 h = 0.1162040607 Simplifying h = 0.1162040607

Solution

The solution to the problem is based on the solutions from the subproblems. h = {0.7171292727, 0.1162040607}

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