7x^2-6x-4=0

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Solution for 7x^2-6x-4=0 equation: 


Simplifying
7x2 + -6x + -4 = 0

Reorder the terms:
-4 + -6x + 7x2 = 0

Solving
-4 + -6x + 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'.
-0.5714285714 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + -0.8571428571x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + -0.8571428571x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + -0.8571428571x + x2 = 0 + 0.5714285714
-0.8571428571x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
-0.8571428571x + x2 = 0.5714285714

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 0.5714285714 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 0.5714285714 + 0.1836734694

Combine like terms: 0.5714285714 + 0.1836734694 = 0.7551020408
0.1836734694 + -0.8571428571x + x2 = 0.7551020408

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 0.7551020408

Calculate the square root of the right side: 0.868966076

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 0.868966076 and -0.868966076.


Subproblem 1
x + -0.4285714286 = 0.868966076

Simplifying
x + -0.4285714286 = 0.868966076

Reorder the terms:
-0.4285714286 + x = 0.868966076

Solving
-0.4285714286 + x = 0.868966076

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = 0.868966076 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = 0.868966076 + 0.4285714286
x = 0.868966076 + 0.4285714286

Combine like terms: 0.868966076 + 0.4285714286 = 1.2975375046
x = 1.2975375046

Simplifying
x = 1.2975375046


Subproblem 2
x + -0.4285714286 = -0.868966076

Simplifying
x + -0.4285714286 = -0.868966076

Reorder the terms:
-0.4285714286 + x = -0.868966076

Solving
-0.4285714286 + x = -0.868966076

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = -0.868966076 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = -0.868966076 + 0.4285714286
x = -0.868966076 + 0.4285714286

Combine like terms: -0.868966076 + 0.4285714286 = -0.4403946474
x = -0.4403946474

Simplifying
x = -0.4403946474


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2975375046, -0.4403946474}

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