7x^2-12=36+7x

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Solution for 7x^2-12=36+7x equation:


Simplifying
7x2 + -12 = 36 + 7x

Reorder the terms:
-12 + 7x2 = 36 + 7x

Solving
-12 + 7x2 = 36 + 7x

Solving for variable 'x'.

Reorder the terms:
-12 + -36 + -7x + 7x2 = 36 + 7x + -36 + -7x

Combine like terms: -12 + -36 = -48
-48 + -7x + 7x2 = 36 + 7x + -36 + -7x

Reorder the terms:
-48 + -7x + 7x2 = 36 + -36 + 7x + -7x

Combine like terms: 36 + -36 = 0
-48 + -7x + 7x2 = 0 + 7x + -7x
-48 + -7x + 7x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-48 + -7x + 7x2 = 0

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

Divide each side by '7'.
-6.857142857 + -1x + x2 = 0

Move the constant term to the right:

Add '6.857142857' to each side of the equation.
-6.857142857 + -1x + 6.857142857 + x2 = 0 + 6.857142857

Reorder the terms:
-6.857142857 + 6.857142857 + -1x + x2 = 0 + 6.857142857

Combine like terms: -6.857142857 + 6.857142857 = 0.000000000
0.000000000 + -1x + x2 = 0 + 6.857142857
-1x + x2 = 0 + 6.857142857

Combine like terms: 0 + 6.857142857 = 6.857142857
-1x + x2 = 6.857142857

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 6.857142857 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 6.857142857 + 0.25

Combine like terms: 6.857142857 + 0.25 = 7.107142857
0.25 + -1x + x2 = 7.107142857

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 7.107142857

Calculate the square root of the right side: 2.665922515

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.665922515 and -2.665922515.

Subproblem 1

x + -0.5 = 2.665922515 Simplifying x + -0.5 = 2.665922515 Reorder the terms: -0.5 + x = 2.665922515 Solving -0.5 + x = 2.665922515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.665922515 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.665922515 + 0.5 x = 2.665922515 + 0.5 Combine like terms: 2.665922515 + 0.5 = 3.165922515 x = 3.165922515 Simplifying x = 3.165922515

Subproblem 2

x + -0.5 = -2.665922515 Simplifying x + -0.5 = -2.665922515 Reorder the terms: -0.5 + x = -2.665922515 Solving -0.5 + x = -2.665922515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.665922515 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.665922515 + 0.5 x = -2.665922515 + 0.5 Combine like terms: -2.665922515 + 0.5 = -2.165922515 x = -2.165922515 Simplifying x = -2.165922515

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.165922515, -2.165922515}

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