-8h^2-4h+9=0

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Solution for -8h^2-4h+9=0 equation:


Simplifying
-8h2 + -4h + 9 = 0

Reorder the terms:
9 + -4h + -8h2 = 0

Solving
9 + -4h + -8h2 = 0

Solving for variable 'h'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.125 + 0.5h + h2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 0.5h + 1.125 + h2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 0.5h + h2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 0.5h + h2 = 0 + 1.125
0.5h + h2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
0.5h + h2 = 1.125

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 = 1.125 + 0.0625

Reorder the terms:
0.0625 + 0.5h + h2 = 1.125 + 0.0625

Combine like terms: 1.125 + 0.0625 = 1.1875
0.0625 + 0.5h + h2 = 1.1875

Factor a perfect square on the left side:
(h + 0.25)(h + 0.25) = 1.1875

Calculate the square root of the right side: 1.089724736

Break this problem into two subproblems by setting 
(h + 0.25) equal to 1.089724736 and -1.089724736.

Subproblem 1

h + 0.25 = 1.089724736 Simplifying h + 0.25 = 1.089724736 Reorder the terms: 0.25 + h = 1.089724736 Solving 0.25 + h = 1.089724736 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 = 1.089724736 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + h = 1.089724736 + -0.25 h = 1.089724736 + -0.25 Combine like terms: 1.089724736 + -0.25 = 0.839724736 h = 0.839724736 Simplifying h = 0.839724736

Subproblem 2

h + 0.25 = -1.089724736 Simplifying h + 0.25 = -1.089724736 Reorder the terms: 0.25 + h = -1.089724736 Solving 0.25 + h = -1.089724736 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 = -1.089724736 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + h = -1.089724736 + -0.25 h = -1.089724736 + -0.25 Combine like terms: -1.089724736 + -0.25 = -1.339724736 h = -1.339724736 Simplifying h = -1.339724736

Solution

The solution to the problem is based on the solutions from the subproblems. h = {0.839724736, -1.339724736}

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