x^2+8.075x=31.36

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Solution for x^2+8.075x=31.36 equation: 


Simplifying
x2 + 8.075x = 31.36

Reorder the terms:
8.075x + x2 = 31.36

Solving
8.075x + x2 = 31.36

Solving for variable 'x'.

Reorder the terms:
-31.36 + 8.075x + x2 = 31.36 + -31.36

Combine like terms: 31.36 + -31.36 = 0.00
-31.36 + 8.075x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '31.36' to each side of the equation.
-31.36 + 8.075x + 31.36 + x2 = 0.00 + 31.36

Reorder the terms:
-31.36 + 31.36 + 8.075x + x2 = 0.00 + 31.36

Combine like terms: -31.36 + 31.36 = 0.00
0.00 + 8.075x + x2 = 0.00 + 31.36
8.075x + x2 = 0.00 + 31.36

Combine like terms: 0.00 + 31.36 = 31.36
8.075x + x2 = 31.36

The x term is 8.075x.  Take half its coefficient (4.0375).
Square it (16.30140625) and add it to both sides.

Add '16.30140625' to each side of the equation.
8.075x + 16.30140625 + x2 = 31.36 + 16.30140625

Reorder the terms:
16.30140625 + 8.075x + x2 = 31.36 + 16.30140625

Combine like terms: 31.36 + 16.30140625 = 47.66140625
16.30140625 + 8.075x + x2 = 47.66140625

Factor a perfect square on the left side:
(x + 4.0375)(x + 4.0375) = 47.66140625

Calculate the square root of the right side: 6.903724086

Break this problem into two subproblems by setting 
(x + 4.0375) equal to 6.903724086 and -6.903724086.


Subproblem 1
x + 4.0375 = 6.903724086

Simplifying
x + 4.0375 = 6.903724086

Reorder the terms:
4.0375 + x = 6.903724086

Solving
4.0375 + x = 6.903724086

Solving for variable 'x'.

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

Add '-4.0375' to each side of the equation.
4.0375 + -4.0375 + x = 6.903724086 + -4.0375

Combine like terms: 4.0375 + -4.0375 = 0.0000
0.0000 + x = 6.903724086 + -4.0375
x = 6.903724086 + -4.0375

Combine like terms: 6.903724086 + -4.0375 = 2.866224086
x = 2.866224086

Simplifying
x = 2.866224086


Subproblem 2
x + 4.0375 = -6.903724086

Simplifying
x + 4.0375 = -6.903724086

Reorder the terms:
4.0375 + x = -6.903724086

Solving
4.0375 + x = -6.903724086

Solving for variable 'x'.

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

Add '-4.0375' to each side of the equation.
4.0375 + -4.0375 + x = -6.903724086 + -4.0375

Combine like terms: 4.0375 + -4.0375 = 0.0000
0.0000 + x = -6.903724086 + -4.0375
x = -6.903724086 + -4.0375

Combine like terms: -6.903724086 + -4.0375 = -10.941224086
x = -10.941224086

Simplifying
x = -10.941224086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.866224086, -10.941224086}

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