4=3x^2-9x

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Solution for 4=3x^2-9x equation:


Simplifying
4 = 3x2 + -9x

Reorder the terms:
4 = -9x + 3x2

Solving
4 = -9x + 3x2

Solving for variable 'x'.

Reorder the terms:
4 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2

Combine like terms: -9x + 9x = 0
4 + 9x + -3x2 = 0 + 3x2 + -3x2
4 + 9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + 9x + -3x2 = 0

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

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

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -3x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -3x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 1.333333333
-3x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-3x + x2 = 1.333333333

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 = 1.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1.333333333 + 2.25

Combine like terms: 1.333333333 + 2.25 = 3.583333333
2.25 + -3x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.892969449 and -1.892969449.

Subproblem 1

x + -1.5 = 1.892969449 Simplifying x + -1.5 = 1.892969449 Reorder the terms: -1.5 + x = 1.892969449 Solving -1.5 + x = 1.892969449 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 = 1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.892969449 + 1.5 x = 1.892969449 + 1.5 Combine like terms: 1.892969449 + 1.5 = 3.392969449 x = 3.392969449 Simplifying x = 3.392969449

Subproblem 2

x + -1.5 = -1.892969449 Simplifying x + -1.5 = -1.892969449 Reorder the terms: -1.5 + x = -1.892969449 Solving -1.5 + x = -1.892969449 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 = -1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.892969449 + 1.5 x = -1.892969449 + 1.5 Combine like terms: -1.892969449 + 1.5 = -0.392969449 x = -0.392969449 Simplifying x = -0.392969449

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.392969449, -0.392969449}

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