12x^2+18x-750=0

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Solution for 12x^2+18x-750=0 equation: 


Simplifying
12x2 + 18x + -750 = 0

Reorder the terms:
-750 + 18x + 12x2 = 0

Solving
-750 + 18x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-125 + 3x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-125 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-125 + 3x + 2x2 = 0

Solving
-125 + 3x + 2x2 = 0

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

Divide each side by '2'.
-62.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '62.5' to each side of the equation.
-62.5 + 1.5x + 62.5 + x2 = 0 + 62.5

Reorder the terms:
-62.5 + 62.5 + 1.5x + x2 = 0 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + 1.5x + x2 = 0 + 62.5
1.5x + x2 = 0 + 62.5

Combine like terms: 0 + 62.5 = 62.5
1.5x + x2 = 62.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 62.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 62.5 + 0.5625

Combine like terms: 62.5 + 0.5625 = 63.0625
0.5625 + 1.5x + x2 = 63.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 63.0625

Calculate the square root of the right side: 7.941190087

Break this problem into two subproblems by setting 
(x + 0.75) equal to 7.941190087 and -7.941190087.


Subproblem 1
x + 0.75 = 7.941190087

Simplifying
x + 0.75 = 7.941190087

Reorder the terms:
0.75 + x = 7.941190087

Solving
0.75 + x = 7.941190087

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 7.941190087 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 7.941190087 + -0.75
x = 7.941190087 + -0.75

Combine like terms: 7.941190087 + -0.75 = 7.191190087
x = 7.191190087

Simplifying
x = 7.191190087


Subproblem 2
x + 0.75 = -7.941190087

Simplifying
x + 0.75 = -7.941190087

Reorder the terms:
0.75 + x = -7.941190087

Solving
0.75 + x = -7.941190087

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -7.941190087 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -7.941190087 + -0.75
x = -7.941190087 + -0.75

Combine like terms: -7.941190087 + -0.75 = -8.691190087
x = -8.691190087

Simplifying
x = -8.691190087


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.191190087, -8.691190087}
Solution
x = {7.191190087, -8.691190087}

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