3x^2-9x=-2

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Solution for 3x^2-9x=-2 equation:


Simplifying
3x2 + -9x = -2

Reorder the terms:
-9x + 3x2 = -2

Solving
-9x + 3x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + -9x + 3x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -9x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3x + x2 = 0 + -0.6666666667
-3x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3x + x2 = -0.6666666667

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.6666666667 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.6666666667 + 2.25

Combine like terms: -0.6666666667 + 2.25 = 1.5833333333
2.25 + -3x + x2 = 1.5833333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.5833333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.258305739 and -1.258305739.

Subproblem 1

x + -1.5 = 1.258305739 Simplifying x + -1.5 = 1.258305739 Reorder the terms: -1.5 + x = 1.258305739 Solving -1.5 + x = 1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.258305739 + 1.5 x = 1.258305739 + 1.5 Combine like terms: 1.258305739 + 1.5 = 2.758305739 x = 2.758305739 Simplifying x = 2.758305739

Subproblem 2

x + -1.5 = -1.258305739 Simplifying x + -1.5 = -1.258305739 Reorder the terms: -1.5 + x = -1.258305739 Solving -1.5 + x = -1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.258305739 + 1.5 x = -1.258305739 + 1.5 Combine like terms: -1.258305739 + 1.5 = 0.241694261 x = 0.241694261 Simplifying x = 0.241694261

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.758305739, 0.241694261}

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