6x^2=5-4x

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


Simplifying
6x2 = 5 + -4x

Solving
6x2 = 5 + -4x

Solving for variable 'x'.

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

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

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