3x^2-7x-37=0

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Solution for 3x^2-7x-37=0 equation: 


Simplifying
3x2 + -7x + -37 = 0

Reorder the terms:
-37 + -7x + 3x2 = 0

Solving
-37 + -7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-12.33333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '12.33333333' to each side of the equation.
-12.33333333 + -2.333333333x + 12.33333333 + x2 = 0 + 12.33333333

Reorder the terms:
-12.33333333 + 12.33333333 + -2.333333333x + x2 = 0 + 12.33333333

Combine like terms: -12.33333333 + 12.33333333 = 0.00000000
0.00000000 + -2.333333333x + x2 = 0 + 12.33333333
-2.333333333x + x2 = 0 + 12.33333333

Combine like terms: 0 + 12.33333333 = 12.33333333
-2.333333333x + x2 = 12.33333333

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 12.33333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 12.33333333 + 1.361111112

Combine like terms: 12.33333333 + 1.361111112 = 13.694444442
1.361111112 + -2.333333333x + x2 = 13.694444442

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 13.694444442

Calculate the square root of the right side: 3.700600552

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 3.700600552 and -3.700600552.


Subproblem 1
x + -1.166666667 = 3.700600552

Simplifying
x + -1.166666667 = 3.700600552

Reorder the terms:
-1.166666667 + x = 3.700600552

Solving
-1.166666667 + x = 3.700600552

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 3.700600552 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 3.700600552 + 1.166666667
x = 3.700600552 + 1.166666667

Combine like terms: 3.700600552 + 1.166666667 = 4.867267219
x = 4.867267219

Simplifying
x = 4.867267219


Subproblem 2
x + -1.166666667 = -3.700600552

Simplifying
x + -1.166666667 = -3.700600552

Reorder the terms:
-1.166666667 + x = -3.700600552

Solving
-1.166666667 + x = -3.700600552

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -3.700600552 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -3.700600552 + 1.166666667
x = -3.700600552 + 1.166666667

Combine like terms: -3.700600552 + 1.166666667 = -2.533933885
x = -2.533933885

Simplifying
x = -2.533933885


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.867267219, -2.533933885}

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