7x^2-3x-1=0

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Solution for 7x^2-3x-1=0 equation: 


Simplifying
7x2 + -3x + -1 = 0

Reorder the terms:
-1 + -3x + 7x2 = 0

Solving
-1 + -3x + 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 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -0.4285714286x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -0.4285714286x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -0.4285714286x + x2 = 0 + 0.1428571429
-0.4285714286x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-0.4285714286x + x2 = 0.1428571429

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 0.1428571429 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 0.1428571429 + 0.04591836735

Combine like terms: 0.1428571429 + 0.04591836735 = 0.18877551025
0.04591836735 + -0.4285714286x + x2 = 0.18877551025

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 0.18877551025

Calculate the square root of the right side: 0.434483038

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 0.434483038 and -0.434483038.


Subproblem 1
x + -0.2142857143 = 0.434483038

Simplifying
x + -0.2142857143 = 0.434483038

Reorder the terms:
-0.2142857143 + x = 0.434483038

Solving
-0.2142857143 + x = 0.434483038

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = 0.434483038 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 0.434483038 + 0.2142857143
x = 0.434483038 + 0.2142857143

Combine like terms: 0.434483038 + 0.2142857143 = 0.6487687523
x = 0.6487687523

Simplifying
x = 0.6487687523


Subproblem 2
x + -0.2142857143 = -0.434483038

Simplifying
x + -0.2142857143 = -0.434483038

Reorder the terms:
-0.2142857143 + x = -0.434483038

Solving
-0.2142857143 + x = -0.434483038

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = -0.434483038 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -0.434483038 + 0.2142857143
x = -0.434483038 + 0.2142857143

Combine like terms: -0.434483038 + 0.2142857143 = -0.2201973237
x = -0.2201973237

Simplifying
x = -0.2201973237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6487687523, -0.2201973237}

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