x^2+5*x-10=8.057319459

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Solution for x^2+5*x-10=8.057319459 equation: 


Simplifying
x2 + 5x + -10 = 8.057319459

Reorder the terms:
-10 + 5x + x2 = 8.057319459

Solving
-10 + 5x + x2 = 8.057319459

Solving for variable 'x'.

Reorder the terms:
-10 + -8.057319459 + 5x + x2 = 8.057319459 + -8.057319459

Combine like terms: -10 + -8.057319459 = -18.057319459
-18.057319459 + 5x + x2 = 8.057319459 + -8.057319459

Combine like terms: 8.057319459 + -8.057319459 = 0.000000000
-18.057319459 + 5x + x2 = 0.000000000

Begin completing the square.

Move the constant term to the right:

Add '18.057319459' to each side of the equation.
-18.057319459 + 5x + 18.057319459 + x2 = 0.000000000 + 18.057319459

Reorder the terms:
-18.057319459 + 18.057319459 + 5x + x2 = 0.000000000 + 18.057319459

Combine like terms: -18.057319459 + 18.057319459 = 0.000000000
0.000000000 + 5x + x2 = 0.000000000 + 18.057319459
5x + x2 = 0.000000000 + 18.057319459

Combine like terms: 0.000000000 + 18.057319459 = 18.057319459
5x + x2 = 18.057319459

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 18.057319459 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 18.057319459 + 6.25

Combine like terms: 18.057319459 + 6.25 = 24.307319459
6.25 + 5x + x2 = 24.307319459

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 24.307319459

Calculate the square root of the right side: 4.930245375

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.930245375 and -4.930245375.


Subproblem 1
x + 2.5 = 4.930245375

Simplifying
x + 2.5 = 4.930245375

Reorder the terms:
2.5 + x = 4.930245375

Solving
2.5 + x = 4.930245375

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.930245375 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.930245375 + -2.5
x = 4.930245375 + -2.5

Combine like terms: 4.930245375 + -2.5 = 2.430245375
x = 2.430245375

Simplifying
x = 2.430245375


Subproblem 2
x + 2.5 = -4.930245375

Simplifying
x + 2.5 = -4.930245375

Reorder the terms:
2.5 + x = -4.930245375

Solving
2.5 + x = -4.930245375

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.930245375 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.930245375 + -2.5
x = -4.930245375 + -2.5

Combine like terms: -4.930245375 + -2.5 = -7.430245375
x = -7.430245375

Simplifying
x = -7.430245375


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.430245375, -7.430245375}

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