8x^2+23.6232x=7x^2-130.3

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Solution for 8x^2+23.6232x=7x^2-130.3 equation:


Simplifying
8x2 + 23.6232x = 7x2 + -130.3

Reorder the terms:
23.6232x + 8x2 = 7x2 + -130.3

Reorder the terms:
23.6232x + 8x2 = -130.3 + 7x2

Solving
23.6232x + 8x2 = -130.3 + 7x2

Solving for variable 'x'.

Reorder the terms:
130.3 + 23.6232x + 8x2 + -7x2 = -130.3 + 7x2 + 130.3 + -7x2

Combine like terms: 8x2 + -7x2 = 1x2
130.3 + 23.6232x + 1x2 = -130.3 + 7x2 + 130.3 + -7x2

Reorder the terms:
130.3 + 23.6232x + 1x2 = -130.3 + 130.3 + 7x2 + -7x2

Combine like terms: -130.3 + 130.3 = 0.0
130.3 + 23.6232x + 1x2 = 0.0 + 7x2 + -7x2
130.3 + 23.6232x + 1x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
130.3 + 23.6232x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-130.3' to each side of the equation.
130.3 + 23.6232x + -130.3 + x2 = 0 + -130.3

Reorder the terms:
130.3 + -130.3 + 23.6232x + x2 = 0 + -130.3

Combine like terms: 130.3 + -130.3 = 0.0
0.0 + 23.6232x + x2 = 0 + -130.3
23.6232x + x2 = 0 + -130.3

Combine like terms: 0 + -130.3 = -130.3
23.6232x + x2 = -130.3

The x term is 23.6232x.  Take half its coefficient (11.8116).
Square it (139.5138946) and add it to both sides.

Add '139.5138946' to each side of the equation.
23.6232x + 139.5138946 + x2 = -130.3 + 139.5138946

Reorder the terms:
139.5138946 + 23.6232x + x2 = -130.3 + 139.5138946

Combine like terms: -130.3 + 139.5138946 = 9.2138946
139.5138946 + 23.6232x + x2 = 9.2138946

Factor a perfect square on the left side:
(x + 11.8116)(x + 11.8116) = 9.2138946

Calculate the square root of the right side: 3.03543977

Break this problem into two subproblems by setting 
(x + 11.8116) equal to 3.03543977 and -3.03543977.

Subproblem 1

x + 11.8116 = 3.03543977 Simplifying x + 11.8116 = 3.03543977 Reorder the terms: 11.8116 + x = 3.03543977 Solving 11.8116 + x = 3.03543977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.8116' to each side of the equation. 11.8116 + -11.8116 + x = 3.03543977 + -11.8116 Combine like terms: 11.8116 + -11.8116 = 0.0000 0.0000 + x = 3.03543977 + -11.8116 x = 3.03543977 + -11.8116 Combine like terms: 3.03543977 + -11.8116 = -8.77616023 x = -8.77616023 Simplifying x = -8.77616023

Subproblem 2

x + 11.8116 = -3.03543977 Simplifying x + 11.8116 = -3.03543977 Reorder the terms: 11.8116 + x = -3.03543977 Solving 11.8116 + x = -3.03543977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.8116' to each side of the equation. 11.8116 + -11.8116 + x = -3.03543977 + -11.8116 Combine like terms: 11.8116 + -11.8116 = 0.0000 0.0000 + x = -3.03543977 + -11.8116 x = -3.03543977 + -11.8116 Combine like terms: -3.03543977 + -11.8116 = -14.84703977 x = -14.84703977 Simplifying x = -14.84703977

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-8.77616023, -14.84703977}

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