4x^2=136+10x

Solution for 4x^2=136+10x equation:

Simplifying
4x2 = 136 + 10x

Solving
4x2 = 136 + 10x

Solving for variable 'x'.

Reorder the terms:
-136 + -10x + 4x2 = 136 + 10x + -136 + -10x

Reorder the terms:
-136 + -10x + 4x2 = 136 + -136 + 10x + -10x

Combine like terms: 136 + -136 = 0
-136 + -10x + 4x2 = 0 + 10x + -10x
-136 + -10x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-136 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + -5x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-68 + -5x + 2x2)' equal to zero and attempt to solve:

Simplifying
-68 + -5x + 2x2 = 0

Solving
-68 + -5x + 2x2 = 0

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

Divide each side by '2'.
-34 + -2.5x + x2 = 0

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -2.5x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -2.5x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -2.5x + x2 = 0 + 34
-2.5x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-2.5x + x2 = 34

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 34 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 34 + 1.5625

Combine like terms: 34 + 1.5625 = 35.5625
1.5625 + -2.5x + x2 = 35.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 35.5625

Calculate the square root of the right side: 5.963430221

Break this problem into two subproblems by setting 
(x + -1.25) equal to 5.963430221 and -5.963430221.

Subproblem 1
x + -1.25 = 5.963430221

Simplifying
x + -1.25 = 5.963430221

Reorder the terms:
-1.25 + x = 5.963430221

Solving
-1.25 + x = 5.963430221

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 5.963430221 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 5.963430221 + 1.25
x = 5.963430221 + 1.25

Combine like terms: 5.963430221 + 1.25 = 7.213430221
x = 7.213430221

Simplifying
x = 7.213430221

Subproblem 2
x + -1.25 = -5.963430221

Simplifying
x + -1.25 = -5.963430221

Reorder the terms:
-1.25 + x = -5.963430221

Solving
-1.25 + x = -5.963430221

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -5.963430221 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -5.963430221 + 1.25
x = -5.963430221 + 1.25

Combine like terms: -5.963430221 + 1.25 = -4.713430221
x = -4.713430221

Simplifying
x = -4.713430221

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.213430221, -4.713430221}
Solution
x = {7.213430221, -4.713430221}