x^2+10x-475=0

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Solution for x^2+10x-475=0 equation: 


Simplifying
x2 + 10x + -475 = 0

Reorder the terms:
-475 + 10x + x2 = 0

Solving
-475 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '475' to each side of the equation.
-475 + 10x + 475 + x2 = 0 + 475

Reorder the terms:
-475 + 475 + 10x + x2 = 0 + 475

Combine like terms: -475 + 475 = 0
0 + 10x + x2 = 0 + 475
10x + x2 = 0 + 475

Combine like terms: 0 + 475 = 475
10x + x2 = 475

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 475 + 25

Reorder the terms:
25 + 10x + x2 = 475 + 25

Combine like terms: 475 + 25 = 500
25 + 10x + x2 = 500

Factor a perfect square on the left side:
(x + 5)(x + 5) = 500

Calculate the square root of the right side: 22.360679775

Break this problem into two subproblems by setting 
(x + 5) equal to 22.360679775 and -22.360679775.


Subproblem 1
x + 5 = 22.360679775

Simplifying
x + 5 = 22.360679775

Reorder the terms:
5 + x = 22.360679775

Solving
5 + x = 22.360679775

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 22.360679775 + -5

Combine like terms: 5 + -5 = 0
0 + x = 22.360679775 + -5
x = 22.360679775 + -5

Combine like terms: 22.360679775 + -5 = 17.360679775
x = 17.360679775

Simplifying
x = 17.360679775


Subproblem 2
x + 5 = -22.360679775

Simplifying
x + 5 = -22.360679775

Reorder the terms:
5 + x = -22.360679775

Solving
5 + x = -22.360679775

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -22.360679775 + -5

Combine like terms: 5 + -5 = 0
0 + x = -22.360679775 + -5
x = -22.360679775 + -5

Combine like terms: -22.360679775 + -5 = -27.360679775
x = -27.360679775

Simplifying
x = -27.360679775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.360679775, -27.360679775}

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