x^2+10x+21=289

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Solution for x^2+10x+21=289 equation: 


Simplifying
x2 + 10x + 21 = 289

Reorder the terms:
21 + 10x + x2 = 289

Solving
21 + 10x + x2 = 289

Solving for variable 'x'.

Reorder the terms:
21 + -289 + 10x + x2 = 289 + -289

Combine like terms: 21 + -289 = -268
-268 + 10x + x2 = 289 + -289

Combine like terms: 289 + -289 = 0
-268 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '268' to each side of the equation.
-268 + 10x + 268 + x2 = 0 + 268

Reorder the terms:
-268 + 268 + 10x + x2 = 0 + 268

Combine like terms: -268 + 268 = 0
0 + 10x + x2 = 0 + 268
10x + x2 = 0 + 268

Combine like terms: 0 + 268 = 268
10x + x2 = 268

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 = 268 + 25

Reorder the terms:
25 + 10x + x2 = 268 + 25

Combine like terms: 268 + 25 = 293
25 + 10x + x2 = 293

Factor a perfect square on the left side:
(x + 5)(x + 5) = 293

Calculate the square root of the right side: 17.117242769

Break this problem into two subproblems by setting 
(x + 5) equal to 17.117242769 and -17.117242769.


Subproblem 1
x + 5 = 17.117242769

Simplifying
x + 5 = 17.117242769

Reorder the terms:
5 + x = 17.117242769

Solving
5 + x = 17.117242769

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 = 17.117242769 + -5

Combine like terms: 5 + -5 = 0
0 + x = 17.117242769 + -5
x = 17.117242769 + -5

Combine like terms: 17.117242769 + -5 = 12.117242769
x = 12.117242769

Simplifying
x = 12.117242769


Subproblem 2
x + 5 = -17.117242769

Simplifying
x + 5 = -17.117242769

Reorder the terms:
5 + x = -17.117242769

Solving
5 + x = -17.117242769

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 = -17.117242769 + -5

Combine like terms: 5 + -5 = 0
0 + x = -17.117242769 + -5
x = -17.117242769 + -5

Combine like terms: -17.117242769 + -5 = -22.117242769
x = -22.117242769

Simplifying
x = -22.117242769


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.117242769, -22.117242769}

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