x^2+10x+21=484

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Solution for x^2+10x+21=484 equation: 


Simplifying
x2 + 10x + 21 = 484

Reorder the terms:
21 + 10x + x2 = 484

Solving
21 + 10x + x2 = 484

Solving for variable 'x'.

Reorder the terms:
21 + -484 + 10x + x2 = 484 + -484

Combine like terms: 21 + -484 = -463
-463 + 10x + x2 = 484 + -484

Combine like terms: 484 + -484 = 0
-463 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '463' to each side of the equation.
-463 + 10x + 463 + x2 = 0 + 463

Reorder the terms:
-463 + 463 + 10x + x2 = 0 + 463

Combine like terms: -463 + 463 = 0
0 + 10x + x2 = 0 + 463
10x + x2 = 0 + 463

Combine like terms: 0 + 463 = 463
10x + x2 = 463

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 = 463 + 25

Reorder the terms:
25 + 10x + x2 = 463 + 25

Combine like terms: 463 + 25 = 488
25 + 10x + x2 = 488

Factor a perfect square on the left side:
(x + 5)(x + 5) = 488

Calculate the square root of the right side: 22.090722034

Break this problem into two subproblems by setting 
(x + 5) equal to 22.090722034 and -22.090722034.


Subproblem 1
x + 5 = 22.090722034

Simplifying
x + 5 = 22.090722034

Reorder the terms:
5 + x = 22.090722034

Solving
5 + x = 22.090722034

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 = 22.090722034 + -5

Combine like terms: 5 + -5 = 0
0 + x = 22.090722034 + -5
x = 22.090722034 + -5

Combine like terms: 22.090722034 + -5 = 17.090722034
x = 17.090722034

Simplifying
x = 17.090722034


Subproblem 2
x + 5 = -22.090722034

Simplifying
x + 5 = -22.090722034

Reorder the terms:
5 + x = -22.090722034

Solving
5 + x = -22.090722034

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 = -22.090722034 + -5

Combine like terms: 5 + -5 = 0
0 + x = -22.090722034 + -5
x = -22.090722034 + -5

Combine like terms: -22.090722034 + -5 = -27.090722034
x = -27.090722034

Simplifying
x = -27.090722034


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.090722034, -27.090722034}

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