x^2+37.32x+144.17=0

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Solution for x^2+37.32x+144.17=0 equation: 


Simplifying
x2 + 37.32x + 144.17 = 0

Reorder the terms:
144.17 + 37.32x + x2 = 0

Solving
144.17 + 37.32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-144.17' to each side of the equation.
144.17 + 37.32x + -144.17 + x2 = 0 + -144.17

Reorder the terms:
144.17 + -144.17 + 37.32x + x2 = 0 + -144.17

Combine like terms: 144.17 + -144.17 = 0.00
0.00 + 37.32x + x2 = 0 + -144.17
37.32x + x2 = 0 + -144.17

Combine like terms: 0 + -144.17 = -144.17
37.32x + x2 = -144.17

The x term is 37.32x.  Take half its coefficient (18.66).
Square it (348.1956) and add it to both sides.

Add '348.1956' to each side of the equation.
37.32x + 348.1956 + x2 = -144.17 + 348.1956

Reorder the terms:
348.1956 + 37.32x + x2 = -144.17 + 348.1956

Combine like terms: -144.17 + 348.1956 = 204.0256
348.1956 + 37.32x + x2 = 204.0256

Factor a perfect square on the left side:
(x + 18.66)(x + 18.66) = 204.0256

Calculate the square root of the right side: 14.283753008

Break this problem into two subproblems by setting 
(x + 18.66) equal to 14.283753008 and -14.283753008.


Subproblem 1
x + 18.66 = 14.283753008

Simplifying
x + 18.66 = 14.283753008

Reorder the terms:
18.66 + x = 14.283753008

Solving
18.66 + x = 14.283753008

Solving for variable 'x'.

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

Add '-18.66' to each side of the equation.
18.66 + -18.66 + x = 14.283753008 + -18.66

Combine like terms: 18.66 + -18.66 = 0.00
0.00 + x = 14.283753008 + -18.66
x = 14.283753008 + -18.66

Combine like terms: 14.283753008 + -18.66 = -4.376246992
x = -4.376246992

Simplifying
x = -4.376246992


Subproblem 2
x + 18.66 = -14.283753008

Simplifying
x + 18.66 = -14.283753008

Reorder the terms:
18.66 + x = -14.283753008

Solving
18.66 + x = -14.283753008

Solving for variable 'x'.

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

Add '-18.66' to each side of the equation.
18.66 + -18.66 + x = -14.283753008 + -18.66

Combine like terms: 18.66 + -18.66 = 0.00
0.00 + x = -14.283753008 + -18.66
x = -14.283753008 + -18.66

Combine like terms: -14.283753008 + -18.66 = -32.943753008
x = -32.943753008

Simplifying
x = -32.943753008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.376246992, -32.943753008}

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