3x^2-7=7-24x

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Solution for 3x^2-7=7-24x equation: 


Simplifying
3x2 + -7 = 7 + -24x

Reorder the terms:
-7 + 3x2 = 7 + -24x

Solving
-7 + 3x2 = 7 + -24x

Solving for variable 'x'.

Reorder the terms:
-7 + -7 + 24x + 3x2 = 7 + -24x + -7 + 24x

Combine like terms: -7 + -7 = -14
-14 + 24x + 3x2 = 7 + -24x + -7 + 24x

Reorder the terms:
-14 + 24x + 3x2 = 7 + -7 + -24x + 24x

Combine like terms: 7 + -7 = 0
-14 + 24x + 3x2 = 0 + -24x + 24x
-14 + 24x + 3x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-14 + 24x + 3x2 = 0

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

Divide each side by '3'.
-4.666666667 + 8x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 8x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 8x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 8x + x2 = 0 + 4.666666667
8x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
8x + x2 = 4.666666667

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 4.666666667 + 16

Reorder the terms:
16 + 8x + x2 = 4.666666667 + 16

Combine like terms: 4.666666667 + 16 = 20.666666667
16 + 8x + x2 = 20.666666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 20.666666667

Calculate the square root of the right side: 4.546060566

Break this problem into two subproblems by setting 
(x + 4) equal to 4.546060566 and -4.546060566.


Subproblem 1
x + 4 = 4.546060566

Simplifying
x + 4 = 4.546060566

Reorder the terms:
4 + x = 4.546060566

Solving
4 + x = 4.546060566

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.546060566 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.546060566 + -4
x = 4.546060566 + -4

Combine like terms: 4.546060566 + -4 = 0.546060566
x = 0.546060566

Simplifying
x = 0.546060566


Subproblem 2
x + 4 = -4.546060566

Simplifying
x + 4 = -4.546060566

Reorder the terms:
4 + x = -4.546060566

Solving
4 + x = -4.546060566

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.546060566 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.546060566 + -4
x = -4.546060566 + -4

Combine like terms: -4.546060566 + -4 = -8.546060566
x = -8.546060566

Simplifying
x = -8.546060566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.546060566, -8.546060566}

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