-15x^2+64x-40=0

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Solution for -15x^2+64x-40=0 equation: 


Simplifying
-15x2 + 64x + -40 = 0

Reorder the terms:
-40 + 64x + -15x2 = 0

Solving
-40 + 64x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
2.666666667 + -4.266666667x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -4.266666667x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -4.266666667x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -4.266666667x + x2 = 0 + -2.666666667
-4.266666667x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-4.266666667x + x2 = -2.666666667

The x term is -4.266666667x.  Take half its coefficient (-2.133333334).
Square it (4.551111114) and add it to both sides.

Add '4.551111114' to each side of the equation.
-4.266666667x + 4.551111114 + x2 = -2.666666667 + 4.551111114

Reorder the terms:
4.551111114 + -4.266666667x + x2 = -2.666666667 + 4.551111114

Combine like terms: -2.666666667 + 4.551111114 = 1.884444447
4.551111114 + -4.266666667x + x2 = 1.884444447

Factor a perfect square on the left side:
(x + -2.133333334)(x + -2.133333334) = 1.884444447

Calculate the square root of the right side: 1.372750686

Break this problem into two subproblems by setting 
(x + -2.133333334) equal to 1.372750686 and -1.372750686.


Subproblem 1
x + -2.133333334 = 1.372750686

Simplifying
x + -2.133333334 = 1.372750686

Reorder the terms:
-2.133333334 + x = 1.372750686

Solving
-2.133333334 + x = 1.372750686

Solving for variable 'x'.

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

Add '2.133333334' to each side of the equation.
-2.133333334 + 2.133333334 + x = 1.372750686 + 2.133333334

Combine like terms: -2.133333334 + 2.133333334 = 0.000000000
0.000000000 + x = 1.372750686 + 2.133333334
x = 1.372750686 + 2.133333334

Combine like terms: 1.372750686 + 2.133333334 = 3.50608402
x = 3.50608402

Simplifying
x = 3.50608402


Subproblem 2
x + -2.133333334 = -1.372750686

Simplifying
x + -2.133333334 = -1.372750686

Reorder the terms:
-2.133333334 + x = -1.372750686

Solving
-2.133333334 + x = -1.372750686

Solving for variable 'x'.

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

Add '2.133333334' to each side of the equation.
-2.133333334 + 2.133333334 + x = -1.372750686 + 2.133333334

Combine like terms: -2.133333334 + 2.133333334 = 0.000000000
0.000000000 + x = -1.372750686 + 2.133333334
x = -1.372750686 + 2.133333334

Combine like terms: -1.372750686 + 2.133333334 = 0.760582648
x = 0.760582648

Simplifying
x = 0.760582648


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.50608402, 0.760582648}

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