2.5x^2-4x-8=0

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Solution for 2.5x^2-4x-8=0 equation: 


Simplifying
2.5x2 + -4x + -8 = 0

Reorder the terms:
-8 + -4x + 2.5x2 = 0

Solving
-8 + -4x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
-3.2 + -1.6x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -1.6x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -1.6x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -1.6x + x2 = 0 + 3.2
-1.6x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-1.6x + x2 = 3.2

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 3.2 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 3.2 + 0.64

Combine like terms: 3.2 + 0.64 = 3.84
0.64 + -1.6x + x2 = 3.84

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 3.84

Calculate the square root of the right side: 1.959591794

Break this problem into two subproblems by setting 
(x + -0.8) equal to 1.959591794 and -1.959591794.


Subproblem 1
x + -0.8 = 1.959591794

Simplifying
x + -0.8 = 1.959591794

Reorder the terms:
-0.8 + x = 1.959591794

Solving
-0.8 + x = 1.959591794

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 1.959591794 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 1.959591794 + 0.8
x = 1.959591794 + 0.8

Combine like terms: 1.959591794 + 0.8 = 2.759591794
x = 2.759591794

Simplifying
x = 2.759591794


Subproblem 2
x + -0.8 = -1.959591794

Simplifying
x + -0.8 = -1.959591794

Reorder the terms:
-0.8 + x = -1.959591794

Solving
-0.8 + x = -1.959591794

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -1.959591794 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -1.959591794 + 0.8
x = -1.959591794 + 0.8

Combine like terms: -1.959591794 + 0.8 = -1.159591794
x = -1.159591794

Simplifying
x = -1.159591794


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.759591794, -1.159591794}

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