4x^2+37x+66=0

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Solution for 4x^2+37x+66=0 equation: 


Simplifying
4x2 + 37x + 66 = 0

Reorder the terms:
66 + 37x + 4x2 = 0

Solving
66 + 37x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
16.5 + 9.25x + x2 = 0

Move the constant term to the right:

Add '-16.5' to each side of the equation.
16.5 + 9.25x + -16.5 + x2 = 0 + -16.5

Reorder the terms:
16.5 + -16.5 + 9.25x + x2 = 0 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + 9.25x + x2 = 0 + -16.5
9.25x + x2 = 0 + -16.5

Combine like terms: 0 + -16.5 = -16.5
9.25x + x2 = -16.5

The x term is 9.25x.  Take half its coefficient (4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
9.25x + 21.390625 + x2 = -16.5 + 21.390625

Reorder the terms:
21.390625 + 9.25x + x2 = -16.5 + 21.390625

Combine like terms: -16.5 + 21.390625 = 4.890625
21.390625 + 9.25x + x2 = 4.890625

Factor a perfect square on the left side:
(x + 4.625)(x + 4.625) = 4.890625

Calculate the square root of the right side: 2.211475752

Break this problem into two subproblems by setting 
(x + 4.625) equal to 2.211475752 and -2.211475752.


Subproblem 1
x + 4.625 = 2.211475752

Simplifying
x + 4.625 = 2.211475752

Reorder the terms:
4.625 + x = 2.211475752

Solving
4.625 + x = 2.211475752

Solving for variable 'x'.

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

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = 2.211475752 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = 2.211475752 + -4.625
x = 2.211475752 + -4.625

Combine like terms: 2.211475752 + -4.625 = -2.413524248
x = -2.413524248

Simplifying
x = -2.413524248


Subproblem 2
x + 4.625 = -2.211475752

Simplifying
x + 4.625 = -2.211475752

Reorder the terms:
4.625 + x = -2.211475752

Solving
4.625 + x = -2.211475752

Solving for variable 'x'.

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

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = -2.211475752 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = -2.211475752 + -4.625
x = -2.211475752 + -4.625

Combine like terms: -2.211475752 + -4.625 = -6.836475752
x = -6.836475752

Simplifying
x = -6.836475752


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.413524248, -6.836475752}

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