x^2+10x+21=729

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Solution for x^2+10x+21=729 equation: 


Simplifying
x2 + 10x + 21 = 729

Reorder the terms:
21 + 10x + x2 = 729

Solving
21 + 10x + x2 = 729

Solving for variable 'x'.

Reorder the terms:
21 + -729 + 10x + x2 = 729 + -729

Combine like terms: 21 + -729 = -708
-708 + 10x + x2 = 729 + -729

Combine like terms: 729 + -729 = 0
-708 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '708' to each side of the equation.
-708 + 10x + 708 + x2 = 0 + 708

Reorder the terms:
-708 + 708 + 10x + x2 = 0 + 708

Combine like terms: -708 + 708 = 0
0 + 10x + x2 = 0 + 708
10x + x2 = 0 + 708

Combine like terms: 0 + 708 = 708
10x + x2 = 708

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 = 708 + 25

Reorder the terms:
25 + 10x + x2 = 708 + 25

Combine like terms: 708 + 25 = 733
25 + 10x + x2 = 733

Factor a perfect square on the left side:
(x + 5)(x + 5) = 733

Calculate the square root of the right side: 27.073972741

Break this problem into two subproblems by setting 
(x + 5) equal to 27.073972741 and -27.073972741.


Subproblem 1
x + 5 = 27.073972741

Simplifying
x + 5 = 27.073972741

Reorder the terms:
5 + x = 27.073972741

Solving
5 + x = 27.073972741

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 = 27.073972741 + -5

Combine like terms: 5 + -5 = 0
0 + x = 27.073972741 + -5
x = 27.073972741 + -5

Combine like terms: 27.073972741 + -5 = 22.073972741
x = 22.073972741

Simplifying
x = 22.073972741


Subproblem 2
x + 5 = -27.073972741

Simplifying
x + 5 = -27.073972741

Reorder the terms:
5 + x = -27.073972741

Solving
5 + x = -27.073972741

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 = -27.073972741 + -5

Combine like terms: 5 + -5 = 0
0 + x = -27.073972741 + -5
x = -27.073972741 + -5

Combine like terms: -27.073972741 + -5 = -32.073972741
x = -32.073972741

Simplifying
x = -32.073972741


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.073972741, -32.073972741}

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