8x^2-x-80=0

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Solution for 8x^2-x-80=0 equation:


Simplifying
8x2 + -1x + -80 = 0

Reorder the terms:
-80 + -1x + 8x2 = 0

Solving
-80 + -1x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-10 + -0.125x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -0.125x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -0.125x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -0.125x + x2 = 0 + 10
-0.125x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-0.125x + x2 = 10

The x term is -0.125x.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125x + 0.00390625 + x2 = 10 + 0.00390625

Reorder the terms:
0.00390625 + -0.125x + x2 = 10 + 0.00390625

Combine like terms: 10 + 0.00390625 = 10.00390625
0.00390625 + -0.125x + x2 = 10.00390625

Factor a perfect square on the left side:
(x + -0.0625)(x + -0.0625) = 10.00390625

Calculate the square root of the right side: 3.162895232

Break this problem into two subproblems by setting 
(x + -0.0625) equal to 3.162895232 and -3.162895232.

Subproblem 1

x + -0.0625 = 3.162895232 Simplifying x + -0.0625 = 3.162895232 Reorder the terms: -0.0625 + x = 3.162895232 Solving -0.0625 + x = 3.162895232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 3.162895232 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 3.162895232 + 0.0625 x = 3.162895232 + 0.0625 Combine like terms: 3.162895232 + 0.0625 = 3.225395232 x = 3.225395232 Simplifying x = 3.225395232

Subproblem 2

x + -0.0625 = -3.162895232 Simplifying x + -0.0625 = -3.162895232 Reorder the terms: -0.0625 + x = -3.162895232 Solving -0.0625 + x = -3.162895232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -3.162895232 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -3.162895232 + 0.0625 x = -3.162895232 + 0.0625 Combine like terms: -3.162895232 + 0.0625 = -3.100395232 x = -3.100395232 Simplifying x = -3.100395232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.225395232, -3.100395232}

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