x^2+10x+21=196

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Solution for x^2+10x+21=196 equation: 


Simplifying
x2 + 10x + 21 = 196

Reorder the terms:
21 + 10x + x2 = 196

Solving
21 + 10x + x2 = 196

Solving for variable 'x'.

Reorder the terms:
21 + -196 + 10x + x2 = 196 + -196

Combine like terms: 21 + -196 = -175
-175 + 10x + x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-175 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + 10x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + 10x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 10x + x2 = 0 + 175
10x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
10x + x2 = 175

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 = 175 + 25

Reorder the terms:
25 + 10x + x2 = 175 + 25

Combine like terms: 175 + 25 = 200
25 + 10x + x2 = 200

Factor a perfect square on the left side:
(x + 5)(x + 5) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(x + 5) equal to 14.142135624 and -14.142135624.


Subproblem 1
x + 5 = 14.142135624

Simplifying
x + 5 = 14.142135624

Reorder the terms:
5 + x = 14.142135624

Solving
5 + x = 14.142135624

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 = 14.142135624 + -5

Combine like terms: 5 + -5 = 0
0 + x = 14.142135624 + -5
x = 14.142135624 + -5

Combine like terms: 14.142135624 + -5 = 9.142135624
x = 9.142135624

Simplifying
x = 9.142135624


Subproblem 2
x + 5 = -14.142135624

Simplifying
x + 5 = -14.142135624

Reorder the terms:
5 + x = -14.142135624

Solving
5 + x = -14.142135624

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 = -14.142135624 + -5

Combine like terms: 5 + -5 = 0
0 + x = -14.142135624 + -5
x = -14.142135624 + -5

Combine like terms: -14.142135624 + -5 = -19.142135624
x = -19.142135624

Simplifying
x = -19.142135624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.142135624, -19.142135624}

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