7x^2+5x-1=0

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Solution for 7x^2+5x-1=0 equation: 


Simplifying
7x2 + 5x + -1 = 0

Reorder the terms:
-1 + 5x + 7x2 = 0

Solving
-1 + 5x + 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'.
-0.1428571429 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.7142857143x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.7142857143x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.7142857143x + x2 = 0 + 0.1428571429
0.7142857143x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.7142857143x + x2 = 0.1428571429

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 0.1428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 0.1428571429 + 0.1275510204

Combine like terms: 0.1428571429 + 0.1275510204 = 0.2704081633
0.1275510204 + 0.7142857143x + x2 = 0.2704081633

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 0.2704081633

Calculate the square root of the right side: 0.520007849

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 0.520007849 and -0.520007849.


Subproblem 1
x + 0.3571428572 = 0.520007849

Simplifying
x + 0.3571428572 = 0.520007849

Reorder the terms:
0.3571428572 + x = 0.520007849

Solving
0.3571428572 + x = 0.520007849

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = 0.520007849 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = 0.520007849 + -0.3571428572
x = 0.520007849 + -0.3571428572

Combine like terms: 0.520007849 + -0.3571428572 = 0.1628649918
x = 0.1628649918

Simplifying
x = 0.1628649918


Subproblem 2
x + 0.3571428572 = -0.520007849

Simplifying
x + 0.3571428572 = -0.520007849

Reorder the terms:
0.3571428572 + x = -0.520007849

Solving
0.3571428572 + x = -0.520007849

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = -0.520007849 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = -0.520007849 + -0.3571428572
x = -0.520007849 + -0.3571428572

Combine like terms: -0.520007849 + -0.3571428572 = -0.8771507062
x = -0.8771507062

Simplifying
x = -0.8771507062


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1628649918, -0.8771507062}

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