-3x^2+6x=-22

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Solution for -3x^2+6x=-22 equation:


Simplifying
-3x2 + 6x = -22

Reorder the terms:
6x + -3x2 = -22

Solving
6x + -3x2 = -22

Solving for variable 'x'.

Reorder the terms:
22 + 6x + -3x2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + 6x + -3x2 = 0

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

Divide each side by '-3'.
-7.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + -2x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + -2x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 7.333333333
-2x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
-2x + x2 = 7.333333333

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 = 7.333333333 + 1

Reorder the terms:
1 + -2x + x2 = 7.333333333 + 1

Combine like terms: 7.333333333 + 1 = 8.333333333
1 + -2x + x2 = 8.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 8.333333333

Calculate the square root of the right side: 2.886751346

Break this problem into two subproblems by setting 
(x + -1) equal to 2.886751346 and -2.886751346.

Subproblem 1

x + -1 = 2.886751346 Simplifying x + -1 = 2.886751346 Reorder the terms: -1 + x = 2.886751346 Solving -1 + x = 2.886751346 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 = 2.886751346 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.886751346 + 1 x = 2.886751346 + 1 Combine like terms: 2.886751346 + 1 = 3.886751346 x = 3.886751346 Simplifying x = 3.886751346

Subproblem 2

x + -1 = -2.886751346 Simplifying x + -1 = -2.886751346 Reorder the terms: -1 + x = -2.886751346 Solving -1 + x = -2.886751346 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 = -2.886751346 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.886751346 + 1 x = -2.886751346 + 1 Combine like terms: -2.886751346 + 1 = -1.886751346 x = -1.886751346 Simplifying x = -1.886751346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.886751346, -1.886751346}

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