3x^2+2x-750=0

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Solution for 3x^2+2x-750=0 equation: 


Simplifying
3x2 + 2x + -750 = 0

Reorder the terms:
-750 + 2x + 3x2 = 0

Solving
-750 + 2x + 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'.
-250 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 0.6666666667x + 250 + x2 = 0 + 250

Reorder the terms:
-250 + 250 + 0.6666666667x + x2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 0.6666666667x + x2 = 0 + 250
0.6666666667x + x2 = 0 + 250

Combine like terms: 0 + 250 = 250
0.6666666667x + x2 = 250

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 250 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 250 + 0.1111111112

Combine like terms: 250 + 0.1111111112 = 250.1111111112
0.1111111112 + 0.6666666667x + x2 = 250.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 250.1111111112

Calculate the square root of the right side: 15.814901552

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 15.814901552 and -15.814901552.


Subproblem 1
x + 0.3333333334 = 15.814901552

Simplifying
x + 0.3333333334 = 15.814901552

Reorder the terms:
0.3333333334 + x = 15.814901552

Solving
0.3333333334 + x = 15.814901552

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 15.814901552 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 15.814901552 + -0.3333333334
x = 15.814901552 + -0.3333333334

Combine like terms: 15.814901552 + -0.3333333334 = 15.4815682186
x = 15.4815682186

Simplifying
x = 15.4815682186


Subproblem 2
x + 0.3333333334 = -15.814901552

Simplifying
x + 0.3333333334 = -15.814901552

Reorder the terms:
0.3333333334 + x = -15.814901552

Solving
0.3333333334 + x = -15.814901552

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -15.814901552 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -15.814901552 + -0.3333333334
x = -15.814901552 + -0.3333333334

Combine like terms: -15.814901552 + -0.3333333334 = -16.1482348854
x = -16.1482348854

Simplifying
x = -16.1482348854


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.4815682186, -16.1482348854}

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