6x^2+2x-48=4+10x

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Solution for 6x^2+2x-48=4+10x equation:


Simplifying
6x2 + 2x + -48 = 4 + 10x

Reorder the terms:
-48 + 2x + 6x2 = 4 + 10x

Solving
-48 + 2x + 6x2 = 4 + 10x

Solving for variable 'x'.

Reorder the terms:
-48 + -4 + 2x + -10x + 6x2 = 4 + 10x + -4 + -10x

Combine like terms: -48 + -4 = -52
-52 + 2x + -10x + 6x2 = 4 + 10x + -4 + -10x

Combine like terms: 2x + -10x = -8x
-52 + -8x + 6x2 = 4 + 10x + -4 + -10x

Reorder the terms:
-52 + -8x + 6x2 = 4 + -4 + 10x + -10x

Combine like terms: 4 + -4 = 0
-52 + -8x + 6x2 = 0 + 10x + -10x
-52 + -8x + 6x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-52 + -8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + -4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-26 + -4x + 3x2 = 0

Solving
-26 + -4x + 3x2 = 0

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

Divide each side by '3'.
-8.666666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '8.666666667' to each side of the equation.
-8.666666667 + -1.333333333x + 8.666666667 + x2 = 0 + 8.666666667

Reorder the terms:
-8.666666667 + 8.666666667 + -1.333333333x + x2 = 0 + 8.666666667

Combine like terms: -8.666666667 + 8.666666667 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 8.666666667
-1.333333333x + x2 = 0 + 8.666666667

Combine like terms: 0 + 8.666666667 = 8.666666667
-1.333333333x + x2 = 8.666666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 8.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 8.666666667 + 0.4444444442

Combine like terms: 8.666666667 + 0.4444444442 = 9.1111111112
0.4444444442 + -1.333333333x + x2 = 9.1111111112

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 9.1111111112

Calculate the square root of the right side: 3.018461713

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 3.018461713 and -3.018461713.


Subproblem 1
x + -0.6666666665 = 3.018461713

Simplifying
x + -0.6666666665 = 3.018461713

Reorder the terms:
-0.6666666665 + x = 3.018461713

Solving
-0.6666666665 + x = 3.018461713

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 3.018461713 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 3.018461713 + 0.6666666665
x = 3.018461713 + 0.6666666665

Combine like terms: 3.018461713 + 0.6666666665 = 3.6851283795
x = 3.6851283795

Simplifying
x = 3.6851283795


Subproblem 2
x + -0.6666666665 = -3.018461713

Simplifying
x + -0.6666666665 = -3.018461713

Reorder the terms:
-0.6666666665 + x = -3.018461713

Solving
-0.6666666665 + x = -3.018461713

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -3.018461713 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -3.018461713 + 0.6666666665
x = -3.018461713 + 0.6666666665

Combine like terms: -3.018461713 + 0.6666666665 = -2.3517950465
x = -2.3517950465

Simplifying
x = -2.3517950465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.6851283795, -2.3517950465}
Solution
x = {3.6851283795, -2.3517950465}

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