x^2+40x+225=0

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Solution for x^2+40x+225=0 equation: 


Simplifying
x2 + 40x + 225 = 0

Reorder the terms:
225 + 40x + x2 = 0

Solving
225 + 40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-225' to each side of the equation.
225 + 40x + -225 + x2 = 0 + -225

Reorder the terms:
225 + -225 + 40x + x2 = 0 + -225

Combine like terms: 225 + -225 = 0
0 + 40x + x2 = 0 + -225
40x + x2 = 0 + -225

Combine like terms: 0 + -225 = -225
40x + x2 = -225

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -225 + 400

Reorder the terms:
400 + 40x + x2 = -225 + 400

Combine like terms: -225 + 400 = 175
400 + 40x + x2 = 175

Factor a perfect square on the left side:
(x + 20)(x + 20) = 175

Calculate the square root of the right side: 13.228756555

Break this problem into two subproblems by setting 
(x + 20) equal to 13.228756555 and -13.228756555.


Subproblem 1
x + 20 = 13.228756555

Simplifying
x + 20 = 13.228756555

Reorder the terms:
20 + x = 13.228756555

Solving
20 + x = 13.228756555

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 13.228756555 + -20

Combine like terms: 20 + -20 = 0
0 + x = 13.228756555 + -20
x = 13.228756555 + -20

Combine like terms: 13.228756555 + -20 = -6.771243445
x = -6.771243445

Simplifying
x = -6.771243445


Subproblem 2
x + 20 = -13.228756555

Simplifying
x + 20 = -13.228756555

Reorder the terms:
20 + x = -13.228756555

Solving
20 + x = -13.228756555

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -13.228756555 + -20

Combine like terms: 20 + -20 = 0
0 + x = -13.228756555 + -20
x = -13.228756555 + -20

Combine like terms: -13.228756555 + -20 = -33.228756555
x = -33.228756555

Simplifying
x = -33.228756555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.771243445, -33.228756555}

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