x^2-10.59x-40.7=0

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Solution for x^2-10.59x-40.7=0 equation: 


Simplifying
x2 + -10.59x + -40.7 = 0

Reorder the terms:
-40.7 + -10.59x + x2 = 0

Solving
-40.7 + -10.59x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40.7' to each side of the equation.
-40.7 + -10.59x + 40.7 + x2 = 0 + 40.7

Reorder the terms:
-40.7 + 40.7 + -10.59x + x2 = 0 + 40.7

Combine like terms: -40.7 + 40.7 = 0.0
0.0 + -10.59x + x2 = 0 + 40.7
-10.59x + x2 = 0 + 40.7

Combine like terms: 0 + 40.7 = 40.7
-10.59x + x2 = 40.7

The x term is -10.59x.  Take half its coefficient (-5.295).
Square it (28.037025) and add it to both sides.

Add '28.037025' to each side of the equation.
-10.59x + 28.037025 + x2 = 40.7 + 28.037025

Reorder the terms:
28.037025 + -10.59x + x2 = 40.7 + 28.037025

Combine like terms: 40.7 + 28.037025 = 68.737025
28.037025 + -10.59x + x2 = 68.737025

Factor a perfect square on the left side:
(x + -5.295)(x + -5.295) = 68.737025

Calculate the square root of the right side: 8.290779517

Break this problem into two subproblems by setting 
(x + -5.295) equal to 8.290779517 and -8.290779517.


Subproblem 1
x + -5.295 = 8.290779517

Simplifying
x + -5.295 = 8.290779517

Reorder the terms:
-5.295 + x = 8.290779517

Solving
-5.295 + x = 8.290779517

Solving for variable 'x'.

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

Add '5.295' to each side of the equation.
-5.295 + 5.295 + x = 8.290779517 + 5.295

Combine like terms: -5.295 + 5.295 = 0.000
0.000 + x = 8.290779517 + 5.295
x = 8.290779517 + 5.295

Combine like terms: 8.290779517 + 5.295 = 13.585779517
x = 13.585779517

Simplifying
x = 13.585779517


Subproblem 2
x + -5.295 = -8.290779517

Simplifying
x + -5.295 = -8.290779517

Reorder the terms:
-5.295 + x = -8.290779517

Solving
-5.295 + x = -8.290779517

Solving for variable 'x'.

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

Add '5.295' to each side of the equation.
-5.295 + 5.295 + x = -8.290779517 + 5.295

Combine like terms: -5.295 + 5.295 = 0.000
0.000 + x = -8.290779517 + 5.295
x = -8.290779517 + 5.295

Combine like terms: -8.290779517 + 5.295 = -2.995779517
x = -2.995779517

Simplifying
x = -2.995779517


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.585779517, -2.995779517}

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