x^2+10x+21=256

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Solution for x^2+10x+21=256 equation: 


Simplifying
x2 + 10x + 21 = 256

Reorder the terms:
21 + 10x + x2 = 256

Solving
21 + 10x + x2 = 256

Solving for variable 'x'.

Reorder the terms:
21 + -256 + 10x + x2 = 256 + -256

Combine like terms: 21 + -256 = -235
-235 + 10x + x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-235 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '235' to each side of the equation.
-235 + 10x + 235 + x2 = 0 + 235

Reorder the terms:
-235 + 235 + 10x + x2 = 0 + 235

Combine like terms: -235 + 235 = 0
0 + 10x + x2 = 0 + 235
10x + x2 = 0 + 235

Combine like terms: 0 + 235 = 235
10x + x2 = 235

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 = 235 + 25

Reorder the terms:
25 + 10x + x2 = 235 + 25

Combine like terms: 235 + 25 = 260
25 + 10x + x2 = 260

Factor a perfect square on the left side:
(x + 5)(x + 5) = 260

Calculate the square root of the right side: 16.124515497

Break this problem into two subproblems by setting 
(x + 5) equal to 16.124515497 and -16.124515497.


Subproblem 1
x + 5 = 16.124515497

Simplifying
x + 5 = 16.124515497

Reorder the terms:
5 + x = 16.124515497

Solving
5 + x = 16.124515497

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 = 16.124515497 + -5

Combine like terms: 5 + -5 = 0
0 + x = 16.124515497 + -5
x = 16.124515497 + -5

Combine like terms: 16.124515497 + -5 = 11.124515497
x = 11.124515497

Simplifying
x = 11.124515497


Subproblem 2
x + 5 = -16.124515497

Simplifying
x + 5 = -16.124515497

Reorder the terms:
5 + x = -16.124515497

Solving
5 + x = -16.124515497

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 = -16.124515497 + -5

Combine like terms: 5 + -5 = 0
0 + x = -16.124515497 + -5
x = -16.124515497 + -5

Combine like terms: -16.124515497 + -5 = -21.124515497
x = -21.124515497

Simplifying
x = -21.124515497


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.124515497, -21.124515497}

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