x^2+10x-291=0

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Solution for x^2+10x-291=0 equation: 


Simplifying
x2 + 10x + -291 = 0

Reorder the terms:
-291 + 10x + x2 = 0

Solving
-291 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '291' to each side of the equation.
-291 + 10x + 291 + x2 = 0 + 291

Reorder the terms:
-291 + 291 + 10x + x2 = 0 + 291

Combine like terms: -291 + 291 = 0
0 + 10x + x2 = 0 + 291
10x + x2 = 0 + 291

Combine like terms: 0 + 291 = 291
10x + x2 = 291

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 = 291 + 25

Reorder the terms:
25 + 10x + x2 = 291 + 25

Combine like terms: 291 + 25 = 316
25 + 10x + x2 = 316

Factor a perfect square on the left side:
(x + 5)(x + 5) = 316

Calculate the square root of the right side: 17.776388835

Break this problem into two subproblems by setting 
(x + 5) equal to 17.776388835 and -17.776388835.


Subproblem 1
x + 5 = 17.776388835

Simplifying
x + 5 = 17.776388835

Reorder the terms:
5 + x = 17.776388835

Solving
5 + x = 17.776388835

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 = 17.776388835 + -5

Combine like terms: 5 + -5 = 0
0 + x = 17.776388835 + -5
x = 17.776388835 + -5

Combine like terms: 17.776388835 + -5 = 12.776388835
x = 12.776388835

Simplifying
x = 12.776388835


Subproblem 2
x + 5 = -17.776388835

Simplifying
x + 5 = -17.776388835

Reorder the terms:
5 + x = -17.776388835

Solving
5 + x = -17.776388835

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 = -17.776388835 + -5

Combine like terms: 5 + -5 = 0
0 + x = -17.776388835 + -5
x = -17.776388835 + -5

Combine like terms: -17.776388835 + -5 = -22.776388835
x = -22.776388835

Simplifying
x = -22.776388835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.776388835, -22.776388835}

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