2.5x^2-12x-8=0

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Solution for 2.5x^2-12x-8=0 equation: 


Simplifying
2.5x2 + -12x + -8 = 0

Reorder the terms:
-8 + -12x + 2.5x2 = 0

Solving
-8 + -12x + 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 + -4.8x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -4.8x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -4.8x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -4.8x + x2 = 0 + 3.2
-4.8x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-4.8x + x2 = 3.2

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = 3.2 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = 3.2 + 5.76

Combine like terms: 3.2 + 5.76 = 8.96
5.76 + -4.8x + x2 = 8.96

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 8.96

Calculate the square root of the right side: 2.993325909

Break this problem into two subproblems by setting 
(x + -2.4) equal to 2.993325909 and -2.993325909.


Subproblem 1
x + -2.4 = 2.993325909

Simplifying
x + -2.4 = 2.993325909

Reorder the terms:
-2.4 + x = 2.993325909

Solving
-2.4 + x = 2.993325909

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 2.993325909 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 2.993325909 + 2.4
x = 2.993325909 + 2.4

Combine like terms: 2.993325909 + 2.4 = 5.393325909
x = 5.393325909

Simplifying
x = 5.393325909


Subproblem 2
x + -2.4 = -2.993325909

Simplifying
x + -2.4 = -2.993325909

Reorder the terms:
-2.4 + x = -2.993325909

Solving
-2.4 + x = -2.993325909

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -2.993325909 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -2.993325909 + 2.4
x = -2.993325909 + 2.4

Combine like terms: -2.993325909 + 2.4 = -0.593325909
x = -0.593325909

Simplifying
x = -0.593325909


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.393325909, -0.593325909}

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