32.4-10x-13x^2=0

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Solution for 32.4-10x-13x^2=0 equation: 


Simplifying
32.4 + -10x + -13x2 = 0

Solving
32.4 + -10x + -13x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-13 the coefficient of the squared term: 

Divide each side by '-13'.
-2.492307692 + 0.7692307692x + x2 = 0

Move the constant term to the right:

Add '2.492307692' to each side of the equation.
-2.492307692 + 0.7692307692x + 2.492307692 + x2 = 0 + 2.492307692

Reorder the terms:
-2.492307692 + 2.492307692 + 0.7692307692x + x2 = 0 + 2.492307692

Combine like terms: -2.492307692 + 2.492307692 = 0.000000000
0.000000000 + 0.7692307692x + x2 = 0 + 2.492307692
0.7692307692x + x2 = 0 + 2.492307692

Combine like terms: 0 + 2.492307692 = 2.492307692
0.7692307692x + x2 = 2.492307692

The x term is 0.7692307692x.  Take half its coefficient (0.3846153846).
Square it (0.1479289941) and add it to both sides.

Add '0.1479289941' to each side of the equation.
0.7692307692x + 0.1479289941 + x2 = 2.492307692 + 0.1479289941

Reorder the terms:
0.1479289941 + 0.7692307692x + x2 = 2.492307692 + 0.1479289941

Combine like terms: 2.492307692 + 0.1479289941 = 2.6402366861
0.1479289941 + 0.7692307692x + x2 = 2.6402366861

Factor a perfect square on the left side:
(x + 0.3846153846)(x + 0.3846153846) = 2.6402366861

Calculate the square root of the right side: 1.624880514

Break this problem into two subproblems by setting 
(x + 0.3846153846) equal to 1.624880514 and -1.624880514.


Subproblem 1
x + 0.3846153846 = 1.624880514

Simplifying
x + 0.3846153846 = 1.624880514

Reorder the terms:
0.3846153846 + x = 1.624880514

Solving
0.3846153846 + x = 1.624880514

Solving for variable 'x'.

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

Add '-0.3846153846' to each side of the equation.
0.3846153846 + -0.3846153846 + x = 1.624880514 + -0.3846153846

Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000
0.0000000000 + x = 1.624880514 + -0.3846153846
x = 1.624880514 + -0.3846153846

Combine like terms: 1.624880514 + -0.3846153846 = 1.2402651294
x = 1.2402651294

Simplifying
x = 1.2402651294


Subproblem 2
x + 0.3846153846 = -1.624880514

Simplifying
x + 0.3846153846 = -1.624880514

Reorder the terms:
0.3846153846 + x = -1.624880514

Solving
0.3846153846 + x = -1.624880514

Solving for variable 'x'.

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

Add '-0.3846153846' to each side of the equation.
0.3846153846 + -0.3846153846 + x = -1.624880514 + -0.3846153846

Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000
0.0000000000 + x = -1.624880514 + -0.3846153846
x = -1.624880514 + -0.3846153846

Combine like terms: -1.624880514 + -0.3846153846 = -2.0094958986
x = -2.0094958986

Simplifying
x = -2.0094958986


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2402651294, -2.0094958986}

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