4x^2+24x+136=16x^2-88x+121

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Solution for 4x^2+24x+136=16x^2-88x+121 equation: 


Simplifying
4x2 + 24x + 136 = 16x2 + -88x + 121

Reorder the terms:
136 + 24x + 4x2 = 16x2 + -88x + 121

Reorder the terms:
136 + 24x + 4x2 = 121 + -88x + 16x2

Solving
136 + 24x + 4x2 = 121 + -88x + 16x2

Solving for variable 'x'.

Reorder the terms:
136 + -121 + 24x + 88x + 4x2 + -16x2 = 121 + -88x + 16x2 + -121 + 88x + -16x2

Combine like terms: 136 + -121 = 15
15 + 24x + 88x + 4x2 + -16x2 = 121 + -88x + 16x2 + -121 + 88x + -16x2

Combine like terms: 24x + 88x = 112x
15 + 112x + 4x2 + -16x2 = 121 + -88x + 16x2 + -121 + 88x + -16x2

Combine like terms: 4x2 + -16x2 = -12x2
15 + 112x + -12x2 = 121 + -88x + 16x2 + -121 + 88x + -16x2

Reorder the terms:
15 + 112x + -12x2 = 121 + -121 + -88x + 88x + 16x2 + -16x2

Combine like terms: 121 + -121 = 0
15 + 112x + -12x2 = 0 + -88x + 88x + 16x2 + -16x2
15 + 112x + -12x2 = -88x + 88x + 16x2 + -16x2

Combine like terms: -88x + 88x = 0
15 + 112x + -12x2 = 0 + 16x2 + -16x2
15 + 112x + -12x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
15 + 112x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-1.25 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -9.333333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -9.333333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -9.333333333x + x2 = 0 + 1.25
-9.333333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-9.333333333x + x2 = 1.25

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = 1.25 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = 1.25 + 21.77777778

Combine like terms: 1.25 + 21.77777778 = 23.02777778
21.77777778 + -9.333333333x + x2 = 23.02777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 23.02777778

Calculate the square root of the right side: 4.798726683

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 4.798726683 and -4.798726683.


Subproblem 1
x + -4.666666667 = 4.798726683

Simplifying
x + -4.666666667 = 4.798726683

Reorder the terms:
-4.666666667 + x = 4.798726683

Solving
-4.666666667 + x = 4.798726683

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 4.798726683 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 4.798726683 + 4.666666667
x = 4.798726683 + 4.666666667

Combine like terms: 4.798726683 + 4.666666667 = 9.46539335
x = 9.46539335

Simplifying
x = 9.46539335


Subproblem 2
x + -4.666666667 = -4.798726683

Simplifying
x + -4.666666667 = -4.798726683

Reorder the terms:
-4.666666667 + x = -4.798726683

Solving
-4.666666667 + x = -4.798726683

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -4.798726683 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -4.798726683 + 4.666666667
x = -4.798726683 + 4.666666667

Combine like terms: -4.798726683 + 4.666666667 = -0.132060016
x = -0.132060016

Simplifying
x = -0.132060016


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.46539335, -0.132060016}

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