x^2+10x+21=576

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Solution for x^2+10x+21=576 equation: 


Simplifying
x2 + 10x + 21 = 576

Reorder the terms:
21 + 10x + x2 = 576

Solving
21 + 10x + x2 = 576

Solving for variable 'x'.

Reorder the terms:
21 + -576 + 10x + x2 = 576 + -576

Combine like terms: 21 + -576 = -555
-555 + 10x + x2 = 576 + -576

Combine like terms: 576 + -576 = 0
-555 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '555' to each side of the equation.
-555 + 10x + 555 + x2 = 0 + 555

Reorder the terms:
-555 + 555 + 10x + x2 = 0 + 555

Combine like terms: -555 + 555 = 0
0 + 10x + x2 = 0 + 555
10x + x2 = 0 + 555

Combine like terms: 0 + 555 = 555
10x + x2 = 555

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 = 555 + 25

Reorder the terms:
25 + 10x + x2 = 555 + 25

Combine like terms: 555 + 25 = 580
25 + 10x + x2 = 580

Factor a perfect square on the left side:
(x + 5)(x + 5) = 580

Calculate the square root of the right side: 24.083189158

Break this problem into two subproblems by setting 
(x + 5) equal to 24.083189158 and -24.083189158.


Subproblem 1
x + 5 = 24.083189158

Simplifying
x + 5 = 24.083189158

Reorder the terms:
5 + x = 24.083189158

Solving
5 + x = 24.083189158

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 = 24.083189158 + -5

Combine like terms: 5 + -5 = 0
0 + x = 24.083189158 + -5
x = 24.083189158 + -5

Combine like terms: 24.083189158 + -5 = 19.083189158
x = 19.083189158

Simplifying
x = 19.083189158


Subproblem 2
x + 5 = -24.083189158

Simplifying
x + 5 = -24.083189158

Reorder the terms:
5 + x = -24.083189158

Solving
5 + x = -24.083189158

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 = -24.083189158 + -5

Combine like terms: 5 + -5 = 0
0 + x = -24.083189158 + -5
x = -24.083189158 + -5

Combine like terms: -24.083189158 + -5 = -29.083189158
x = -29.083189158

Simplifying
x = -29.083189158


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.083189158, -29.083189158}

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