1.5x^2-12x-10=0

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Solution for 1.5x^2-12x-10=0 equation: 


Simplifying
1.5x2 + -12x + -10 = 0

Reorder the terms:
-10 + -12x + 1.5x2 = 0

Solving
-10 + -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'.
-6.666666667 + -8x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -8x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -8x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -8x + x2 = 0 + 6.666666667
-8x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-8x + x2 = 6.666666667

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 = 6.666666667 + 16

Reorder the terms:
16 + -8x + x2 = 6.666666667 + 16

Combine like terms: 6.666666667 + 16 = 22.666666667
16 + -8x + x2 = 22.666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 22.666666667

Calculate the square root of the right side: 4.760952286

Break this problem into two subproblems by setting 
(x + -4) equal to 4.760952286 and -4.760952286.


Subproblem 1
x + -4 = 4.760952286

Simplifying
x + -4 = 4.760952286

Reorder the terms:
-4 + x = 4.760952286

Solving
-4 + x = 4.760952286

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 = 4.760952286 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.760952286 + 4
x = 4.760952286 + 4

Combine like terms: 4.760952286 + 4 = 8.760952286
x = 8.760952286

Simplifying
x = 8.760952286


Subproblem 2
x + -4 = -4.760952286

Simplifying
x + -4 = -4.760952286

Reorder the terms:
-4 + x = -4.760952286

Solving
-4 + x = -4.760952286

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 = -4.760952286 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.760952286 + 4
x = -4.760952286 + 4

Combine like terms: -4.760952286 + 4 = -0.760952286
x = -0.760952286

Simplifying
x = -0.760952286


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.760952286, -0.760952286}

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