1.5x^2-12x-14=0

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Solution for 1.5x^2-12x-14=0 equation: 


Simplifying
1.5x2 + -12x + -14 = 0

Reorder the terms:
-14 + -12x + 1.5x2 = 0

Solving
-14 + -12x + 1.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.5'.
-9.333333333 + -8x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + -8x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + -8x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + -8x + x2 = 0 + 9.333333333
-8x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
-8x + x2 = 9.333333333

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 9.333333333 + 16

Reorder the terms:
16 + -8x + x2 = 9.333333333 + 16

Combine like terms: 9.333333333 + 16 = 25.333333333
16 + -8x + x2 = 25.333333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 25.333333333

Calculate the square root of the right side: 5.033222957

Break this problem into two subproblems by setting 
(x + -4) equal to 5.033222957 and -5.033222957.


Subproblem 1
x + -4 = 5.033222957

Simplifying
x + -4 = 5.033222957

Reorder the terms:
-4 + x = 5.033222957

Solving
-4 + x = 5.033222957

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 5.033222957 + 4

Combine like terms: -4 + 4 = 0
0 + x = 5.033222957 + 4
x = 5.033222957 + 4

Combine like terms: 5.033222957 + 4 = 9.033222957
x = 9.033222957

Simplifying
x = 9.033222957


Subproblem 2
x + -4 = -5.033222957

Simplifying
x + -4 = -5.033222957

Reorder the terms:
-4 + x = -5.033222957

Solving
-4 + x = -5.033222957

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -5.033222957 + 4

Combine like terms: -4 + 4 = 0
0 + x = -5.033222957 + 4
x = -5.033222957 + 4

Combine like terms: -5.033222957 + 4 = -1.033222957
x = -1.033222957

Simplifying
x = -1.033222957


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.033222957, -1.033222957}

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