x^2+45x+304=0

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Solution for x^2+45x+304=0 equation: 


Simplifying
x2 + 45x + 304 = 0

Reorder the terms:
304 + 45x + x2 = 0

Solving
304 + 45x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-304' to each side of the equation.
304 + 45x + -304 + x2 = 0 + -304

Reorder the terms:
304 + -304 + 45x + x2 = 0 + -304

Combine like terms: 304 + -304 = 0
0 + 45x + x2 = 0 + -304
45x + x2 = 0 + -304

Combine like terms: 0 + -304 = -304
45x + x2 = -304

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = -304 + 506.25

Reorder the terms:
506.25 + 45x + x2 = -304 + 506.25

Combine like terms: -304 + 506.25 = 202.25
506.25 + 45x + x2 = 202.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + 22.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
x + 22.5 = 14.221462653

Simplifying
x + 22.5 = 14.221462653

Reorder the terms:
22.5 + x = 14.221462653

Solving
22.5 + x = 14.221462653

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 14.221462653 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 14.221462653 + -22.5
x = 14.221462653 + -22.5

Combine like terms: 14.221462653 + -22.5 = -8.278537347
x = -8.278537347

Simplifying
x = -8.278537347


Subproblem 2
x + 22.5 = -14.221462653

Simplifying
x + 22.5 = -14.221462653

Reorder the terms:
22.5 + x = -14.221462653

Solving
22.5 + x = -14.221462653

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -14.221462653 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -14.221462653 + -22.5
x = -14.221462653 + -22.5

Combine like terms: -14.221462653 + -22.5 = -36.721462653
x = -36.721462653

Simplifying
x = -36.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.278537347, -36.721462653}

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