5-6x^2=4x

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Solution for 5-6x^2=4x equation: 


Simplifying
5 + -6x2 = 4x

Solving
5 + -6x2 = 4x

Solving for variable 'x'.

Reorder the terms:
5 + -4x + -6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
5 + -4x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.8333333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 0.6666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 0.6666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.8333333333
0.6666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
0.6666666667x + x2 = 0.8333333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.8333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.8333333333 + 0.1111111112

Combine like terms: 0.8333333333 + 0.1111111112 = 0.9444444445
0.1111111112 + 0.6666666667x + x2 = 0.9444444445

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.9444444445

Calculate the square root of the right side: 0.971825316

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.971825316 and -0.971825316.


Subproblem 1
x + 0.3333333334 = 0.971825316

Simplifying
x + 0.3333333334 = 0.971825316

Reorder the terms:
0.3333333334 + x = 0.971825316

Solving
0.3333333334 + x = 0.971825316

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.971825316 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.971825316 + -0.3333333334
x = 0.971825316 + -0.3333333334

Combine like terms: 0.971825316 + -0.3333333334 = 0.6384919826
x = 0.6384919826

Simplifying
x = 0.6384919826


Subproblem 2
x + 0.3333333334 = -0.971825316

Simplifying
x + 0.3333333334 = -0.971825316

Reorder the terms:
0.3333333334 + x = -0.971825316

Solving
0.3333333334 + x = -0.971825316

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.971825316 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.971825316 + -0.3333333334
x = -0.971825316 + -0.3333333334

Combine like terms: -0.971825316 + -0.3333333334 = -1.3051586494
x = -1.3051586494

Simplifying
x = -1.3051586494


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6384919826, -1.3051586494}

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