75x^2+734x-80=0

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Solution for 75x^2+734x-80=0 equation: 


Simplifying
75x2 + 734x + -80 = 0

Reorder the terms:
-80 + 734x + 75x2 = 0

Solving
-80 + 734x + 75x2 = 0

Solving for variable 'x'.

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

Divide each side by '75'.
-1.066666667 + 9.786666667x + x2 = 0

Move the constant term to the right:

Add '1.066666667' to each side of the equation.
-1.066666667 + 9.786666667x + 1.066666667 + x2 = 0 + 1.066666667

Reorder the terms:
-1.066666667 + 1.066666667 + 9.786666667x + x2 = 0 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + 9.786666667x + x2 = 0 + 1.066666667
9.786666667x + x2 = 0 + 1.066666667

Combine like terms: 0 + 1.066666667 = 1.066666667
9.786666667x + x2 = 1.066666667

The x term is 9.786666667x.  Take half its coefficient (4.893333334).
Square it (23.94471112) and add it to both sides.

Add '23.94471112' to each side of the equation.
9.786666667x + 23.94471112 + x2 = 1.066666667 + 23.94471112

Reorder the terms:
23.94471112 + 9.786666667x + x2 = 1.066666667 + 23.94471112

Combine like terms: 1.066666667 + 23.94471112 = 25.011377787
23.94471112 + 9.786666667x + x2 = 25.011377787

Factor a perfect square on the left side:
(x + 4.893333334)(x + 4.893333334) = 25.011377787

Calculate the square root of the right side: 5.001137649

Break this problem into two subproblems by setting 
(x + 4.893333334) equal to 5.001137649 and -5.001137649.


Subproblem 1
x + 4.893333334 = 5.001137649

Simplifying
x + 4.893333334 = 5.001137649

Reorder the terms:
4.893333334 + x = 5.001137649

Solving
4.893333334 + x = 5.001137649

Solving for variable 'x'.

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

Add '-4.893333334' to each side of the equation.
4.893333334 + -4.893333334 + x = 5.001137649 + -4.893333334

Combine like terms: 4.893333334 + -4.893333334 = 0.000000000
0.000000000 + x = 5.001137649 + -4.893333334
x = 5.001137649 + -4.893333334

Combine like terms: 5.001137649 + -4.893333334 = 0.107804315
x = 0.107804315

Simplifying
x = 0.107804315


Subproblem 2
x + 4.893333334 = -5.001137649

Simplifying
x + 4.893333334 = -5.001137649

Reorder the terms:
4.893333334 + x = -5.001137649

Solving
4.893333334 + x = -5.001137649

Solving for variable 'x'.

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

Add '-4.893333334' to each side of the equation.
4.893333334 + -4.893333334 + x = -5.001137649 + -4.893333334

Combine like terms: 4.893333334 + -4.893333334 = 0.000000000
0.000000000 + x = -5.001137649 + -4.893333334
x = -5.001137649 + -4.893333334

Combine like terms: -5.001137649 + -4.893333334 = -9.894470983
x = -9.894470983

Simplifying
x = -9.894470983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.107804315, -9.894470983}

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