15x^2-64x-24=0

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Solution for 15x^2-64x-24=0 equation:


Simplifying
15x2 + -64x + -24 = 0

Reorder the terms:
-24 + -64x + 15x2 = 0

Solving
-24 + -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'.
-1.6 + -4.266666667x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -4.266666667x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -4.266666667x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -4.266666667x + x2 = 0 + 1.6
-4.266666667x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-4.266666667x + x2 = 1.6

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 = 1.6 + 4.551111114

Reorder the terms:
4.551111114 + -4.266666667x + x2 = 1.6 + 4.551111114

Combine like terms: 1.6 + 4.551111114 = 6.151111114
4.551111114 + -4.266666667x + x2 = 6.151111114

Factor a perfect square on the left side:
(x + -2.133333334)(x + -2.133333334) = 6.151111114

Calculate the square root of the right side: 2.480143366

Break this problem into two subproblems by setting 
(x + -2.133333334) equal to 2.480143366 and -2.480143366.

Subproblem 1

x + -2.133333334 = 2.480143366 Simplifying x + -2.133333334 = 2.480143366 Reorder the terms: -2.133333334 + x = 2.480143366 Solving -2.133333334 + x = 2.480143366 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 = 2.480143366 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = 2.480143366 + 2.133333334 x = 2.480143366 + 2.133333334 Combine like terms: 2.480143366 + 2.133333334 = 4.6134767 x = 4.6134767 Simplifying x = 4.6134767

Subproblem 2

x + -2.133333334 = -2.480143366 Simplifying x + -2.133333334 = -2.480143366 Reorder the terms: -2.133333334 + x = -2.480143366 Solving -2.133333334 + x = -2.480143366 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 = -2.480143366 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = -2.480143366 + 2.133333334 x = -2.480143366 + 2.133333334 Combine like terms: -2.480143366 + 2.133333334 = -0.346810032 x = -0.346810032 Simplifying x = -0.346810032

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.6134767, -0.346810032}

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