3x^2-9x^2-3x+20=0

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Solution for 3x^2-9x^2-3x+20=0 equation:


Simplifying
3x2 + -9x2 + -3x + 20 = 0

Reorder the terms:
20 + -3x + 3x2 + -9x2 = 0

Combine like terms: 3x2 + -9x2 = -6x2
20 + -3x + -6x2 = 0

Solving
20 + -3x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-3.333333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 0.5x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 0.5x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + 3.333333333
0.5x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
0.5x + x2 = 3.333333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 3.333333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.333333333 + 0.0625

Combine like terms: 3.333333333 + 0.0625 = 3.395833333
0.0625 + 0.5x + x2 = 3.395833333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.395833333

Calculate the square root of the right side: 1.842778699

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.842778699 and -1.842778699.

Subproblem 1

x + 0.25 = 1.842778699 Simplifying x + 0.25 = 1.842778699 Reorder the terms: 0.25 + x = 1.842778699 Solving 0.25 + x = 1.842778699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.842778699 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.842778699 + -0.25 x = 1.842778699 + -0.25 Combine like terms: 1.842778699 + -0.25 = 1.592778699 x = 1.592778699 Simplifying x = 1.592778699

Subproblem 2

x + 0.25 = -1.842778699 Simplifying x + 0.25 = -1.842778699 Reorder the terms: 0.25 + x = -1.842778699 Solving 0.25 + x = -1.842778699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.842778699 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.842778699 + -0.25 x = -1.842778699 + -0.25 Combine like terms: -1.842778699 + -0.25 = -2.092778699 x = -2.092778699 Simplifying x = -2.092778699

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.592778699, -2.092778699}

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