3x^2-4x=90

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Solution for 3x^2-4x=90 equation:


Simplifying
3x2 + -4x = 90

Reorder the terms:
-4x + 3x2 = 90

Solving
-4x + 3x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -4x + 3x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -4x + 3x2 = 0

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

Divide each side by '3'.
-30 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -1.333333333x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -1.333333333x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1.333333333x + x2 = 0 + 30
-1.333333333x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-1.333333333x + x2 = 30

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 30 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 30 + 0.4444444442

Combine like terms: 30 + 0.4444444442 = 30.4444444442
0.4444444442 + -1.333333333x + x2 = 30.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 30.4444444442

Calculate the square root of the right side: 5.517648452

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 5.517648452 and -5.517648452.

Subproblem 1

x + -0.6666666665 = 5.517648452 Simplifying x + -0.6666666665 = 5.517648452 Reorder the terms: -0.6666666665 + x = 5.517648452 Solving -0.6666666665 + x = 5.517648452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 5.517648452 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 5.517648452 + 0.6666666665 x = 5.517648452 + 0.6666666665 Combine like terms: 5.517648452 + 0.6666666665 = 6.1843151185 x = 6.1843151185 Simplifying x = 6.1843151185

Subproblem 2

x + -0.6666666665 = -5.517648452 Simplifying x + -0.6666666665 = -5.517648452 Reorder the terms: -0.6666666665 + x = -5.517648452 Solving -0.6666666665 + x = -5.517648452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -5.517648452 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -5.517648452 + 0.6666666665 x = -5.517648452 + 0.6666666665 Combine like terms: -5.517648452 + 0.6666666665 = -4.8509817855 x = -4.8509817855 Simplifying x = -4.8509817855

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.1843151185, -4.8509817855}

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