4x^2+32x+37=0

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Solution for 4x^2+32x+37=0 equation: 


Simplifying
4x2 + 32x + 37 = 0

Reorder the terms:
37 + 32x + 4x2 = 0

Solving
37 + 32x + 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'.
9.25 + 8x + x2 = 0

Move the constant term to the right:

Add '-9.25' to each side of the equation.
9.25 + 8x + -9.25 + x2 = 0 + -9.25

Reorder the terms:
9.25 + -9.25 + 8x + x2 = 0 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + 8x + x2 = 0 + -9.25
8x + x2 = 0 + -9.25

Combine like terms: 0 + -9.25 = -9.25
8x + x2 = -9.25

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -9.25 + 16

Reorder the terms:
16 + 8x + x2 = -9.25 + 16

Combine like terms: -9.25 + 16 = 6.75
16 + 8x + x2 = 6.75

Factor a perfect square on the left side:
(x + 4)(x + 4) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(x + 4) equal to 2.598076211 and -2.598076211.


Subproblem 1
x + 4 = 2.598076211

Simplifying
x + 4 = 2.598076211

Reorder the terms:
4 + x = 2.598076211

Solving
4 + x = 2.598076211

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 2.598076211 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.598076211 + -4
x = 2.598076211 + -4

Combine like terms: 2.598076211 + -4 = -1.401923789
x = -1.401923789

Simplifying
x = -1.401923789


Subproblem 2
x + 4 = -2.598076211

Simplifying
x + 4 = -2.598076211

Reorder the terms:
4 + x = -2.598076211

Solving
4 + x = -2.598076211

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -2.598076211 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.598076211 + -4
x = -2.598076211 + -4

Combine like terms: -2.598076211 + -4 = -6.598076211
x = -6.598076211

Simplifying
x = -6.598076211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.401923789, -6.598076211}

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