-2x^2+13x-3=0

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Solution for -2x^2+13x-3=0 equation: 


Simplifying
-2x2 + 13x + -3 = 0

Reorder the terms:
-3 + 13x + -2x2 = 0

Solving
-3 + 13x + -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'.
1.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -6.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -6.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -6.5x + x2 = 0 + -1.5
-6.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-6.5x + x2 = -1.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -1.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -1.5 + 10.5625

Combine like terms: -1.5 + 10.5625 = 9.0625
10.5625 + -6.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.010398645 and -3.010398645.


Subproblem 1
x + -3.25 = 3.010398645

Simplifying
x + -3.25 = 3.010398645

Reorder the terms:
-3.25 + x = 3.010398645

Solving
-3.25 + x = 3.010398645

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.010398645 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.010398645 + 3.25
x = 3.010398645 + 3.25

Combine like terms: 3.010398645 + 3.25 = 6.260398645
x = 6.260398645

Simplifying
x = 6.260398645


Subproblem 2
x + -3.25 = -3.010398645

Simplifying
x + -3.25 = -3.010398645

Reorder the terms:
-3.25 + x = -3.010398645

Solving
-3.25 + x = -3.010398645

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.010398645 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.010398645 + 3.25
x = -3.010398645 + 3.25

Combine like terms: -3.010398645 + 3.25 = 0.239601355
x = 0.239601355

Simplifying
x = 0.239601355


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.260398645, 0.239601355}

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