x^2+10x-207=0

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Solution for x^2+10x-207=0 equation: 


Simplifying
x2 + 10x + -207 = 0

Reorder the terms:
-207 + 10x + x2 = 0

Solving
-207 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '207' to each side of the equation.
-207 + 10x + 207 + x2 = 0 + 207

Reorder the terms:
-207 + 207 + 10x + x2 = 0 + 207

Combine like terms: -207 + 207 = 0
0 + 10x + x2 = 0 + 207
10x + x2 = 0 + 207

Combine like terms: 0 + 207 = 207
10x + x2 = 207

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 = 207 + 25

Reorder the terms:
25 + 10x + x2 = 207 + 25

Combine like terms: 207 + 25 = 232
25 + 10x + x2 = 232

Factor a perfect square on the left side:
(x + 5)(x + 5) = 232

Calculate the square root of the right side: 15.231546212

Break this problem into two subproblems by setting 
(x + 5) equal to 15.231546212 and -15.231546212.


Subproblem 1
x + 5 = 15.231546212

Simplifying
x + 5 = 15.231546212

Reorder the terms:
5 + x = 15.231546212

Solving
5 + x = 15.231546212

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 = 15.231546212 + -5

Combine like terms: 5 + -5 = 0
0 + x = 15.231546212 + -5
x = 15.231546212 + -5

Combine like terms: 15.231546212 + -5 = 10.231546212
x = 10.231546212

Simplifying
x = 10.231546212


Subproblem 2
x + 5 = -15.231546212

Simplifying
x + 5 = -15.231546212

Reorder the terms:
5 + x = -15.231546212

Solving
5 + x = -15.231546212

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 = -15.231546212 + -5

Combine like terms: 5 + -5 = 0
0 + x = -15.231546212 + -5
x = -15.231546212 + -5

Combine like terms: -15.231546212 + -5 = -20.231546212
x = -20.231546212

Simplifying
x = -20.231546212


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.231546212, -20.231546212}

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