8x^2-40x-15=0

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Solution for 8x^2-40x-15=0 equation: 


Simplifying
8x2 + -40x + -15 = 0

Reorder the terms:
-15 + -40x + 8x2 = 0

Solving
-15 + -40x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.875 + -5x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -5x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -5x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -5x + x2 = 0 + 1.875
-5x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-5x + x2 = 1.875

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 1.875 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1.875 + 6.25

Combine like terms: 1.875 + 6.25 = 8.125
6.25 + -5x + x2 = 8.125

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.125

Calculate the square root of the right side: 2.850438563

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.850438563 and -2.850438563.


Subproblem 1
x + -2.5 = 2.850438563

Simplifying
x + -2.5 = 2.850438563

Reorder the terms:
-2.5 + x = 2.850438563

Solving
-2.5 + x = 2.850438563

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.850438563 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.850438563 + 2.5
x = 2.850438563 + 2.5

Combine like terms: 2.850438563 + 2.5 = 5.350438563
x = 5.350438563

Simplifying
x = 5.350438563


Subproblem 2
x + -2.5 = -2.850438563

Simplifying
x + -2.5 = -2.850438563

Reorder the terms:
-2.5 + x = -2.850438563

Solving
-2.5 + x = -2.850438563

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.850438563 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.850438563 + 2.5
x = -2.850438563 + 2.5

Combine like terms: -2.850438563 + 2.5 = -0.350438563
x = -0.350438563

Simplifying
x = -0.350438563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.350438563, -0.350438563}

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