h^2-8h-3=0

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Solution for h^2-8h-3=0 equation:


Simplifying
h2 + -8h + -3 = 0

Reorder the terms:
-3 + -8h + h2 = 0

Solving
-3 + -8h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8h + 3 + h2 = 0 + 3

Reorder the terms:
-3 + 3 + -8h + h2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8h + h2 = 0 + 3
-8h + h2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8h + h2 = 3

The h term is -8h.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8h + 16 + h2 = 3 + 16

Reorder the terms:
16 + -8h + h2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8h + h2 = 19

Factor a perfect square on the left side:
(h + -4)(h + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(h + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1

h + -4 = 4.358898944 Simplifying h + -4 = 4.358898944 Reorder the terms: -4 + h = 4.358898944 Solving -4 + h = 4.358898944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + h = 4.358898944 + 4 h = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 h = 8.358898944 Simplifying h = 8.358898944

Subproblem 2

h + -4 = -4.358898944 Simplifying h + -4 = -4.358898944 Reorder the terms: -4 + h = -4.358898944 Solving -4 + h = -4.358898944 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + h = -4.358898944 + 4 h = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 h = -0.358898944 Simplifying h = -0.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. h = {8.358898944, -0.358898944}

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