-7h^2+7h+5=0

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Solution for -7h^2+7h+5=0 equation:


Simplifying
-7h2 + 7h + 5 = 0

Reorder the terms:
5 + 7h + -7h2 = 0

Solving
5 + 7h + -7h2 = 0

Solving for variable 'h'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.7142857143 + -1h + h2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -1h + 0.7142857143 + h2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -1h + h2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -1h + h2 = 0 + 0.7142857143
-1h + h2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-1h + h2 = 0.7142857143

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 = 0.7142857143 + 0.25

Reorder the terms:
0.25 + -1h + h2 = 0.7142857143 + 0.25

Combine like terms: 0.7142857143 + 0.25 = 0.9642857143
0.25 + -1h + h2 = 0.9642857143

Factor a perfect square on the left side:
(h + -0.5)(h + -0.5) = 0.9642857143

Calculate the square root of the right side: 0.981980506

Break this problem into two subproblems by setting 
(h + -0.5) equal to 0.981980506 and -0.981980506.

Subproblem 1

h + -0.5 = 0.981980506 Simplifying h + -0.5 = 0.981980506 Reorder the terms: -0.5 + h = 0.981980506 Solving -0.5 + h = 0.981980506 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 = 0.981980506 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + h = 0.981980506 + 0.5 h = 0.981980506 + 0.5 Combine like terms: 0.981980506 + 0.5 = 1.481980506 h = 1.481980506 Simplifying h = 1.481980506

Subproblem 2

h + -0.5 = -0.981980506 Simplifying h + -0.5 = -0.981980506 Reorder the terms: -0.5 + h = -0.981980506 Solving -0.5 + h = -0.981980506 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 = -0.981980506 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + h = -0.981980506 + 0.5 h = -0.981980506 + 0.5 Combine like terms: -0.981980506 + 0.5 = -0.481980506 h = -0.481980506 Simplifying h = -0.481980506

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1.481980506, -0.481980506}

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