-2x^2+6.5x-5=0

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Solution for -2x^2+6.5x-5=0 equation: 


Simplifying
-2x2 + 6.5x + -5 = 0

Reorder the terms:
-5 + 6.5x + -2x2 = 0

Solving
-5 + 6.5x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2.5 + -3.25x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3.25x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3.25x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3.25x + x2 = 0 + -2.5
-3.25x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3.25x + x2 = -2.5

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = -2.5 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = -2.5 + 2.640625

Combine like terms: -2.5 + 2.640625 = 0.140625
2.640625 + -3.25x + x2 = 0.140625

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(x + -1.625) equal to 0.375 and -0.375.


Subproblem 1
x + -1.625 = 0.375

Simplifying
x + -1.625 = 0.375

Reorder the terms:
-1.625 + x = 0.375

Solving
-1.625 + x = 0.375

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = 0.375 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = 0.375 + 1.625
x = 0.375 + 1.625

Combine like terms: 0.375 + 1.625 = 2
x = 2

Simplifying
x = 2


Subproblem 2
x + -1.625 = -0.375

Simplifying
x + -1.625 = -0.375

Reorder the terms:
-1.625 + x = -0.375

Solving
-1.625 + x = -0.375

Solving for variable 'x'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + x = -0.375 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + x = -0.375 + 1.625
x = -0.375 + 1.625

Combine like terms: -0.375 + 1.625 = 1.25
x = 1.25

Simplifying
x = 1.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, 1.25}

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