x^2+10x+21=676

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Solution for x^2+10x+21=676 equation: 


Simplifying
x2 + 10x + 21 = 676

Reorder the terms:
21 + 10x + x2 = 676

Solving
21 + 10x + x2 = 676

Solving for variable 'x'.

Reorder the terms:
21 + -676 + 10x + x2 = 676 + -676

Combine like terms: 21 + -676 = -655
-655 + 10x + x2 = 676 + -676

Combine like terms: 676 + -676 = 0
-655 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '655' to each side of the equation.
-655 + 10x + 655 + x2 = 0 + 655

Reorder the terms:
-655 + 655 + 10x + x2 = 0 + 655

Combine like terms: -655 + 655 = 0
0 + 10x + x2 = 0 + 655
10x + x2 = 0 + 655

Combine like terms: 0 + 655 = 655
10x + x2 = 655

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 = 655 + 25

Reorder the terms:
25 + 10x + x2 = 655 + 25

Combine like terms: 655 + 25 = 680
25 + 10x + x2 = 680

Factor a perfect square on the left side:
(x + 5)(x + 5) = 680

Calculate the square root of the right side: 26.076809621

Break this problem into two subproblems by setting 
(x + 5) equal to 26.076809621 and -26.076809621.


Subproblem 1
x + 5 = 26.076809621

Simplifying
x + 5 = 26.076809621

Reorder the terms:
5 + x = 26.076809621

Solving
5 + x = 26.076809621

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 = 26.076809621 + -5

Combine like terms: 5 + -5 = 0
0 + x = 26.076809621 + -5
x = 26.076809621 + -5

Combine like terms: 26.076809621 + -5 = 21.076809621
x = 21.076809621

Simplifying
x = 21.076809621


Subproblem 2
x + 5 = -26.076809621

Simplifying
x + 5 = -26.076809621

Reorder the terms:
5 + x = -26.076809621

Solving
5 + x = -26.076809621

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 = -26.076809621 + -5

Combine like terms: 5 + -5 = 0
0 + x = -26.076809621 + -5
x = -26.076809621 + -5

Combine like terms: -26.076809621 + -5 = -31.076809621
x = -31.076809621

Simplifying
x = -31.076809621


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.076809621, -31.076809621}

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