2x^2-13x-10=0

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


Simplifying
2x2 + -13x + -10 = 0

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

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

Move the constant term to the right:

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

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

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

Combine like terms: 0 + 5 = 5
-6.5x + x2 = 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 = 5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 5 + 10.5625

Combine like terms: 5 + 10.5625 = 15.5625
10.5625 + -6.5x + x2 = 15.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.94493346 and -3.94493346.


Subproblem 1
x + -3.25 = 3.94493346

Simplifying
x + -3.25 = 3.94493346

Reorder the terms:
-3.25 + x = 3.94493346

Solving
-3.25 + x = 3.94493346

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 = 3.94493346 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.94493346 + 3.25
x = 3.94493346 + 3.25

Combine like terms: 3.94493346 + 3.25 = 7.19493346
x = 7.19493346

Simplifying
x = 7.19493346


Subproblem 2
x + -3.25 = -3.94493346

Simplifying
x + -3.25 = -3.94493346

Reorder the terms:
-3.25 + x = -3.94493346

Solving
-3.25 + x = -3.94493346

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 = -3.94493346 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.94493346 + 3.25
x = -3.94493346 + 3.25

Combine like terms: -3.94493346 + 3.25 = -0.69493346
x = -0.69493346

Simplifying
x = -0.69493346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.19493346, -0.69493346}

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