0=x^2+80x+900

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Solution for 0=x^2+80x+900 equation: 


Simplifying
0 = x2 + 80x + 900

Reorder the terms:
0 = 900 + 80x + x2

Solving
0 = 900 + 80x + x2

Solving for variable 'x'.

Combine like terms: 0 + -900 = -900
-900 + -80x + -1x2 = 900 + 80x + x2 + -900 + -80x + -1x2

Reorder the terms:
-900 + -80x + -1x2 = 900 + -900 + 80x + -80x + x2 + -1x2

Combine like terms: 900 + -900 = 0
-900 + -80x + -1x2 = 0 + 80x + -80x + x2 + -1x2
-900 + -80x + -1x2 = 80x + -80x + x2 + -1x2

Combine like terms: 80x + -80x = 0
-900 + -80x + -1x2 = 0 + x2 + -1x2
-900 + -80x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-900 + -80x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(900 + 80x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(900 + 80x + x2)' equal to zero and attempt to solve:

Simplifying
900 + 80x + x2 = 0

Solving
900 + 80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-900' to each side of the equation.
900 + 80x + -900 + x2 = 0 + -900

Reorder the terms:
900 + -900 + 80x + x2 = 0 + -900

Combine like terms: 900 + -900 = 0
0 + 80x + x2 = 0 + -900
80x + x2 = 0 + -900

Combine like terms: 0 + -900 = -900
80x + x2 = -900

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = -900 + 1600

Reorder the terms:
1600 + 80x + x2 = -900 + 1600

Combine like terms: -900 + 1600 = 700
1600 + 80x + x2 = 700

Factor a perfect square on the left side:
(x + 40)(x + 40) = 700

Calculate the square root of the right side: 26.457513111

Break this problem into two subproblems by setting 
(x + 40) equal to 26.457513111 and -26.457513111.


Subproblem 1
x + 40 = 26.457513111

Simplifying
x + 40 = 26.457513111

Reorder the terms:
40 + x = 26.457513111

Solving
40 + x = 26.457513111

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-40' to each side of the equation.
40 + -40 + x = 26.457513111 + -40

Combine like terms: 40 + -40 = 0
0 + x = 26.457513111 + -40
x = 26.457513111 + -40

Combine like terms: 26.457513111 + -40 = -13.542486889
x = -13.542486889

Simplifying
x = -13.542486889


Subproblem 2
x + 40 = -26.457513111

Simplifying
x + 40 = -26.457513111

Reorder the terms:
40 + x = -26.457513111

Solving
40 + x = -26.457513111

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-40' to each side of the equation.
40 + -40 + x = -26.457513111 + -40

Combine like terms: 40 + -40 = 0
0 + x = -26.457513111 + -40
x = -26.457513111 + -40

Combine like terms: -26.457513111 + -40 = -66.457513111
x = -66.457513111

Simplifying
x = -66.457513111


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-13.542486889, -66.457513111}
Solution
x = {-13.542486889, -66.457513111}

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