2x^2+10x-13=0

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Solution for 2x^2+10x-13=0 equation: 


Simplifying
2x2 + 10x + -13 = 0

Reorder the terms:
-13 + 10x + 2x2 = 0

Solving
-13 + 10x + 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'.
-6.5 + 5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 5x + 6.5 + x2 = 0 + 6.5

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

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 5x + x2 = 0 + 6.5
5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
5x + x2 = 6.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 6.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 6.5 + 6.25

Combine like terms: 6.5 + 6.25 = 12.75
6.25 + 5x + x2 = 12.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.570714214 and -3.570714214.


Subproblem 1
x + 2.5 = 3.570714214

Simplifying
x + 2.5 = 3.570714214

Reorder the terms:
2.5 + x = 3.570714214

Solving
2.5 + x = 3.570714214

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.570714214 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.570714214 + -2.5
x = 3.570714214 + -2.5

Combine like terms: 3.570714214 + -2.5 = 1.070714214
x = 1.070714214

Simplifying
x = 1.070714214


Subproblem 2
x + 2.5 = -3.570714214

Simplifying
x + 2.5 = -3.570714214

Reorder the terms:
2.5 + x = -3.570714214

Solving
2.5 + x = -3.570714214

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.570714214 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.570714214 + -2.5
x = -3.570714214 + -2.5

Combine like terms: -3.570714214 + -2.5 = -6.070714214
x = -6.070714214

Simplifying
x = -6.070714214


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.070714214, -6.070714214}

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