8x^2-78x-10=0

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Solution for 8x^2-78x-10=0 equation: 


Simplifying
8x2 + -78x + -10 = 0

Reorder the terms:
-10 + -78x + 8x2 = 0

Solving
-10 + -78x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -39x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -39x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + -39x + 4x2 = 0

Solving
-5 + -39x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + -9.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -9.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -9.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -9.75x + x2 = 0 + 1.25
-9.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-9.75x + x2 = 1.25

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = 1.25 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = 1.25 + 23.765625

Combine like terms: 1.25 + 23.765625 = 25.015625
23.765625 + -9.75x + x2 = 25.015625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 25.015625

Calculate the square root of the right side: 5.001562256

Break this problem into two subproblems by setting 
(x + -4.875) equal to 5.001562256 and -5.001562256.


Subproblem 1
x + -4.875 = 5.001562256

Simplifying
x + -4.875 = 5.001562256

Reorder the terms:
-4.875 + x = 5.001562256

Solving
-4.875 + x = 5.001562256

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = 5.001562256 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = 5.001562256 + 4.875
x = 5.001562256 + 4.875

Combine like terms: 5.001562256 + 4.875 = 9.876562256
x = 9.876562256

Simplifying
x = 9.876562256


Subproblem 2
x + -4.875 = -5.001562256

Simplifying
x + -4.875 = -5.001562256

Reorder the terms:
-4.875 + x = -5.001562256

Solving
-4.875 + x = -5.001562256

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = -5.001562256 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = -5.001562256 + 4.875
x = -5.001562256 + 4.875

Combine like terms: -5.001562256 + 4.875 = -0.126562256
x = -0.126562256

Simplifying
x = -0.126562256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.876562256, -0.126562256}
Solution
x = {9.876562256, -0.126562256}

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