8x^2-20x+2x-15=0

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Solution for 8x^2-20x+2x-15=0 equation: 


Simplifying
8x2 + -20x + 2x + -15 = 0

Reorder the terms:
-15 + -20x + 2x + 8x2 = 0

Combine like terms: -20x + 2x = -18x
-15 + -18x + 8x2 = 0

Solving
-15 + -18x + 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 + -2.25x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -2.25x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -2.25x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -2.25x + x2 = 0 + 1.875
-2.25x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-2.25x + x2 = 1.875

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 1.875 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 1.875 + 1.265625

Combine like terms: 1.875 + 1.265625 = 3.140625
1.265625 + -2.25x + x2 = 3.140625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 3.140625

Calculate the square root of the right side: 1.77218086

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.77218086 and -1.77218086.


Subproblem 1
x + -1.125 = 1.77218086

Simplifying
x + -1.125 = 1.77218086

Reorder the terms:
-1.125 + x = 1.77218086

Solving
-1.125 + x = 1.77218086

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 1.77218086 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.77218086 + 1.125
x = 1.77218086 + 1.125

Combine like terms: 1.77218086 + 1.125 = 2.89718086
x = 2.89718086

Simplifying
x = 2.89718086


Subproblem 2
x + -1.125 = -1.77218086

Simplifying
x + -1.125 = -1.77218086

Reorder the terms:
-1.125 + x = -1.77218086

Solving
-1.125 + x = -1.77218086

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -1.77218086 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.77218086 + 1.125
x = -1.77218086 + 1.125

Combine like terms: -1.77218086 + 1.125 = -0.64718086
x = -0.64718086

Simplifying
x = -0.64718086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.89718086, -0.64718086}

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