3x^2=7-7x

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


Simplifying
3x2 = 7 + -7x

Solving
3x2 = 7 + -7x

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '3'.
-2.333333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 2.333333333x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 2.333333333x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 2.333333333
2.333333333x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
2.333333333x + x2 = 2.333333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 2.333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 2.333333333 + 1.361111112

Combine like terms: 2.333333333 + 1.361111112 = 3.694444445
1.361111112 + 2.333333333x + x2 = 3.694444445

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 3.694444445

Calculate the square root of the right side: 1.922093766

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.922093766 and -1.922093766.


Subproblem 1
x + 1.166666667 = 1.922093766

Simplifying
x + 1.166666667 = 1.922093766

Reorder the terms:
1.166666667 + x = 1.922093766

Solving
1.166666667 + x = 1.922093766

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.922093766 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.922093766 + -1.166666667
x = 1.922093766 + -1.166666667

Combine like terms: 1.922093766 + -1.166666667 = 0.755427099
x = 0.755427099

Simplifying
x = 0.755427099


Subproblem 2
x + 1.166666667 = -1.922093766

Simplifying
x + 1.166666667 = -1.922093766

Reorder the terms:
1.166666667 + x = -1.922093766

Solving
1.166666667 + x = -1.922093766

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.922093766 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.922093766 + -1.166666667
x = -1.922093766 + -1.166666667

Combine like terms: -1.922093766 + -1.166666667 = -3.088760433
x = -3.088760433

Simplifying
x = -3.088760433


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.755427099, -3.088760433}

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