3x^2-9x=50

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Solution for 3x^2-9x=50 equation:


Simplifying
3x2 + -9x = 50

Reorder the terms:
-9x + 3x2 = 50

Solving
-9x + 3x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + -9x + 3x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + -9x + 3x2 = 0

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

Divide each side by '3'.
-16.66666667 + -3x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -3x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -3x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -3x + x2 = 0 + 16.66666667
-3x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-3x + x2 = 16.66666667

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 = 16.66666667 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 16.66666667 + 2.25

Combine like terms: 16.66666667 + 2.25 = 18.91666667
2.25 + -3x + x2 = 18.91666667

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 18.91666667

Calculate the square root of the right side: 4.349329451

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.349329451 and -4.349329451.

Subproblem 1

x + -1.5 = 4.349329451 Simplifying x + -1.5 = 4.349329451 Reorder the terms: -1.5 + x = 4.349329451 Solving -1.5 + x = 4.349329451 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 = 4.349329451 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.349329451 + 1.5 x = 4.349329451 + 1.5 Combine like terms: 4.349329451 + 1.5 = 5.849329451 x = 5.849329451 Simplifying x = 5.849329451

Subproblem 2

x + -1.5 = -4.349329451 Simplifying x + -1.5 = -4.349329451 Reorder the terms: -1.5 + x = -4.349329451 Solving -1.5 + x = -4.349329451 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 = -4.349329451 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.349329451 + 1.5 x = -4.349329451 + 1.5 Combine like terms: -4.349329451 + 1.5 = -2.849329451 x = -2.849329451 Simplifying x = -2.849329451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.849329451, -2.849329451}

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