-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 = 7.217777781
4.551111114 + -4.266666667x + x2 = 7.217777781

Factor a perfect square on the left side:
(x + -2.133333334)(x + -2.133333334) = 7.217777781

Calculate the square root of the right side: 2.686592225

Break this problem into two subproblems by setting 
(x + -2.133333334) equal to 2.686592225 and -2.686592225.


Subproblem 1
x + -2.133333334 = 2.686592225

Simplifying
x + -2.133333334 = 2.686592225

Reorder the terms:
-2.133333334 + x = 2.686592225

Solving
-2.133333334 + x = 2.686592225

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 = 2.686592225 + 2.133333334

Combine like terms: -2.133333334 + 2.133333334 = 0.000000000
0.000000000 + x = 2.686592225 + 2.133333334
x = 2.686592225 + 2.133333334

Combine like terms: 2.686592225 + 2.133333334 = 4.819925559
x = 4.819925559

Simplifying
x = 4.819925559


Subproblem 2
x + -2.133333334 = -2.686592225

Simplifying
x + -2.133333334 = -2.686592225

Reorder the terms:
-2.133333334 + x = -2.686592225

Solving
-2.133333334 + x = -2.686592225

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 = -2.686592225 + 2.133333334

Combine like terms: -2.133333334 + 2.133333334 = 0.000000000
0.000000000 + x = -2.686592225 + 2.133333334
x = -2.686592225 + 2.133333334

Combine like terms: -2.686592225 + 2.133333334 = -0.553258891
x = -0.553258891

Simplifying
x = -0.553258891


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.819925559, -0.553258891}

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