10x^2+13x-7=0

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Solution for 10x^2+13x-7=0 equation: 


Simplifying
10x2 + 13x + -7 = 0

Reorder the terms:
-7 + 13x + 10x2 = 0

Solving
-7 + 13x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-0.7 + 1.3x + x2 = 0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + 1.3x + 0.7 + x2 = 0 + 0.7

Reorder the terms:
-0.7 + 0.7 + 1.3x + x2 = 0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + 1.3x + x2 = 0 + 0.7
1.3x + x2 = 0 + 0.7

Combine like terms: 0 + 0.7 = 0.7
1.3x + x2 = 0.7

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 0.7 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 0.7 + 0.4225

Combine like terms: 0.7 + 0.4225 = 1.1225
0.4225 + 1.3x + x2 = 1.1225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 1.1225

Calculate the square root of the right side: 1.059481005

Break this problem into two subproblems by setting 
(x + 0.65) equal to 1.059481005 and -1.059481005.


Subproblem 1
x + 0.65 = 1.059481005

Simplifying
x + 0.65 = 1.059481005

Reorder the terms:
0.65 + x = 1.059481005

Solving
0.65 + x = 1.059481005

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 1.059481005 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 1.059481005 + -0.65
x = 1.059481005 + -0.65

Combine like terms: 1.059481005 + -0.65 = 0.409481005
x = 0.409481005

Simplifying
x = 0.409481005


Subproblem 2
x + 0.65 = -1.059481005

Simplifying
x + 0.65 = -1.059481005

Reorder the terms:
0.65 + x = -1.059481005

Solving
0.65 + x = -1.059481005

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -1.059481005 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -1.059481005 + -0.65
x = -1.059481005 + -0.65

Combine like terms: -1.059481005 + -0.65 = -1.709481005
x = -1.709481005

Simplifying
x = -1.709481005


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.409481005, -1.709481005}

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