-6x^2-4x+15=0

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Solution for -6x^2-4x+15=0 equation: 


Simplifying
-6x2 + -4x + 15 = 0

Reorder the terms:
15 + -4x + -6x2 = 0

Solving
15 + -4x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-2.5 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.6666666667x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.6666666667x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.6666666667x + x2 = 0 + 2.5
0.6666666667x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.6666666667x + x2 = 2.5

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 = 2.5 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 2.5 + 0.1111111112

Combine like terms: 2.5 + 0.1111111112 = 2.6111111112
0.1111111112 + 0.6666666667x + x2 = 2.6111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 2.6111111112

Calculate the square root of the right side: 1.615893286

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.615893286 and -1.615893286.


Subproblem 1
x + 0.3333333334 = 1.615893286

Simplifying
x + 0.3333333334 = 1.615893286

Reorder the terms:
0.3333333334 + x = 1.615893286

Solving
0.3333333334 + x = 1.615893286

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 = 1.615893286 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.615893286 + -0.3333333334
x = 1.615893286 + -0.3333333334

Combine like terms: 1.615893286 + -0.3333333334 = 1.2825599526
x = 1.2825599526

Simplifying
x = 1.2825599526


Subproblem 2
x + 0.3333333334 = -1.615893286

Simplifying
x + 0.3333333334 = -1.615893286

Reorder the terms:
0.3333333334 + x = -1.615893286

Solving
0.3333333334 + x = -1.615893286

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 = -1.615893286 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.615893286 + -0.3333333334
x = -1.615893286 + -0.3333333334

Combine like terms: -1.615893286 + -0.3333333334 = -1.9492266194
x = -1.9492266194

Simplifying
x = -1.9492266194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2825599526, -1.9492266194}

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