3x^2+44x=97

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Solution for 3x^2+44x=97 equation: 


Simplifying
3x2 + 44x = 97

Reorder the terms:
44x + 3x2 = 97

Solving
44x + 3x2 = 97

Solving for variable 'x'.

Reorder the terms:
-97 + 44x + 3x2 = 97 + -97

Combine like terms: 97 + -97 = 0
-97 + 44x + 3x2 = 0

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

Divide each side by '3'.
-32.33333333 + 14.66666667x + x2 = 0

Move the constant term to the right:

Add '32.33333333' to each side of the equation.
-32.33333333 + 14.66666667x + 32.33333333 + x2 = 0 + 32.33333333

Reorder the terms:
-32.33333333 + 32.33333333 + 14.66666667x + x2 = 0 + 32.33333333

Combine like terms: -32.33333333 + 32.33333333 = 0.00000000
0.00000000 + 14.66666667x + x2 = 0 + 32.33333333
14.66666667x + x2 = 0 + 32.33333333

Combine like terms: 0 + 32.33333333 = 32.33333333
14.66666667x + x2 = 32.33333333

The x term is 14.66666667x.  Take half its coefficient (7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
14.66666667x + 53.77777780 + x2 = 32.33333333 + 53.77777780

Reorder the terms:
53.77777780 + 14.66666667x + x2 = 32.33333333 + 53.77777780

Combine like terms: 32.33333333 + 53.77777780 = 86.11111113
53.77777780 + 14.66666667x + x2 = 86.11111113

Factor a perfect square on the left side:
(x + 7.333333335)(x + 7.333333335) = 86.11111113

Calculate the square root of the right side: 9.279607272

Break this problem into two subproblems by setting 
(x + 7.333333335) equal to 9.279607272 and -9.279607272.


Subproblem 1
x + 7.333333335 = 9.279607272

Simplifying
x + 7.333333335 = 9.279607272

Reorder the terms:
7.333333335 + x = 9.279607272

Solving
7.333333335 + x = 9.279607272

Solving for variable 'x'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + x = 9.279607272 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = 9.279607272 + -7.333333335
x = 9.279607272 + -7.333333335

Combine like terms: 9.279607272 + -7.333333335 = 1.946273937
x = 1.946273937

Simplifying
x = 1.946273937


Subproblem 2
x + 7.333333335 = -9.279607272

Simplifying
x + 7.333333335 = -9.279607272

Reorder the terms:
7.333333335 + x = -9.279607272

Solving
7.333333335 + x = -9.279607272

Solving for variable 'x'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + x = -9.279607272 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = -9.279607272 + -7.333333335
x = -9.279607272 + -7.333333335

Combine like terms: -9.279607272 + -7.333333335 = -16.612940607
x = -16.612940607

Simplifying
x = -16.612940607


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.946273937, -16.612940607}

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