4h^2-2h-19=0

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Solution for 4h^2-2h-19=0 equation:


Simplifying
4h2 + -2h + -19 = 0

Reorder the terms:
-19 + -2h + 4h2 = 0

Solving
-19 + -2h + 4h2 = 0

Solving for variable 'h'.

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

Divide each side by '4'.
-4.75 + -0.5h + h2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + -0.5h + 4.75 + h2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + -0.5h + h2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + -0.5h + h2 = 0 + 4.75
-0.5h + h2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
-0.5h + h2 = 4.75

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 = 4.75 + 0.0625

Reorder the terms:
0.0625 + -0.5h + h2 = 4.75 + 0.0625

Combine like terms: 4.75 + 0.0625 = 4.8125
0.0625 + -0.5h + h2 = 4.8125

Factor a perfect square on the left side:
(h + -0.25)(h + -0.25) = 4.8125

Calculate the square root of the right side: 2.193741097

Break this problem into two subproblems by setting 
(h + -0.25) equal to 2.193741097 and -2.193741097.

Subproblem 1

h + -0.25 = 2.193741097 Simplifying h + -0.25 = 2.193741097 Reorder the terms: -0.25 + h = 2.193741097 Solving -0.25 + h = 2.193741097 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 = 2.193741097 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + h = 2.193741097 + 0.25 h = 2.193741097 + 0.25 Combine like terms: 2.193741097 + 0.25 = 2.443741097 h = 2.443741097 Simplifying h = 2.443741097

Subproblem 2

h + -0.25 = -2.193741097 Simplifying h + -0.25 = -2.193741097 Reorder the terms: -0.25 + h = -2.193741097 Solving -0.25 + h = -2.193741097 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 = -2.193741097 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + h = -2.193741097 + 0.25 h = -2.193741097 + 0.25 Combine like terms: -2.193741097 + 0.25 = -1.943741097 h = -1.943741097 Simplifying h = -1.943741097

Solution

The solution to the problem is based on the solutions from the subproblems. h = {2.443741097, -1.943741097}

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