7x^2+10x-2=0

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


Simplifying
7x2 + 10x + -2 = 0

Reorder the terms:
-2 + 10x + 7x2 = 0

Solving
-2 + 10x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.2857142857 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 1.428571429x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 1.428571429x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 1.428571429x + x2 = 0 + 0.2857142857
1.428571429x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
1.428571429x + x2 = 0.2857142857

The x term is 1.428571429x.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429x + 0.5102040819 + x2 = 0.2857142857 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = 0.2857142857 + 0.5102040819

Combine like terms: 0.2857142857 + 0.5102040819 = 0.7959183676
0.5102040819 + 1.428571429x + x2 = 0.7959183676

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 0.7959183676

Calculate the square root of the right side: 0.892142571

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 0.892142571 and -0.892142571.


Subproblem 1
x + 0.7142857145 = 0.892142571

Simplifying
x + 0.7142857145 = 0.892142571

Reorder the terms:
0.7142857145 + x = 0.892142571

Solving
0.7142857145 + x = 0.892142571

Solving for variable 'x'.

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

Add '-0.7142857145' to each side of the equation.
0.7142857145 + -0.7142857145 + x = 0.892142571 + -0.7142857145

Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000
0.0000000000 + x = 0.892142571 + -0.7142857145
x = 0.892142571 + -0.7142857145

Combine like terms: 0.892142571 + -0.7142857145 = 0.1778568565
x = 0.1778568565

Simplifying
x = 0.1778568565


Subproblem 2
x + 0.7142857145 = -0.892142571

Simplifying
x + 0.7142857145 = -0.892142571

Reorder the terms:
0.7142857145 + x = -0.892142571

Solving
0.7142857145 + x = -0.892142571

Solving for variable 'x'.

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

Add '-0.7142857145' to each side of the equation.
0.7142857145 + -0.7142857145 + x = -0.892142571 + -0.7142857145

Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000
0.0000000000 + x = -0.892142571 + -0.7142857145
x = -0.892142571 + -0.7142857145

Combine like terms: -0.892142571 + -0.7142857145 = -1.6064282855
x = -1.6064282855

Simplifying
x = -1.6064282855


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1778568565, -1.6064282855}

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