3x^2=4-6x

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Solution for 3x^2=4-6x equation:


Simplifying
3x2 = 4 + -6x

Solving
3x2 = 4 + -6x

Solving for variable 'x'.

Reorder the terms:
-4 + 6x + 3x2 = 4 + -6x + -4 + 6x

Reorder the terms:
-4 + 6x + 3x2 = 4 + -4 + -6x + 6x

Combine like terms: 4 + -4 = 0
-4 + 6x + 3x2 = 0 + -6x + 6x
-4 + 6x + 3x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-4 + 6x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 2x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 2x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.333333333
2x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
2x + x2 = 1.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 1.333333333 + 1

Combine like terms: 1.333333333 + 1 = 2.333333333
1 + 2x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + 1) equal to 1.527525232 and -1.527525232.

Subproblem 1

x + 1 = 1.527525232 Simplifying x + 1 = 1.527525232 Reorder the terms: 1 + x = 1.527525232 Solving 1 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.527525232 + -1 x = 1.527525232 + -1 Combine like terms: 1.527525232 + -1 = 0.527525232 x = 0.527525232 Simplifying x = 0.527525232

Subproblem 2

x + 1 = -1.527525232 Simplifying x + 1 = -1.527525232 Reorder the terms: 1 + x = -1.527525232 Solving 1 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.527525232 + -1 x = -1.527525232 + -1 Combine like terms: -1.527525232 + -1 = -2.527525232 x = -2.527525232 Simplifying x = -2.527525232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.527525232, -2.527525232}

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