3x^2-32x=-65

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Solution for 3x^2-32x=-65 equation:


Simplifying
3x2 + -32x = -65

Reorder the terms:
-32x + 3x2 = -65

Solving
-32x + 3x2 = -65

Solving for variable 'x'.

Reorder the terms:
65 + -32x + 3x2 = -65 + 65

Combine like terms: -65 + 65 = 0
65 + -32x + 3x2 = 0

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

Divide each side by '3'.
21.66666667 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '-21.66666667' to each side of the equation.
21.66666667 + -10.66666667x + -21.66666667 + x2 = 0 + -21.66666667

Reorder the terms:
21.66666667 + -21.66666667 + -10.66666667x + x2 = 0 + -21.66666667

Combine like terms: 21.66666667 + -21.66666667 = 0.00000000
0.00000000 + -10.66666667x + x2 = 0 + -21.66666667
-10.66666667x + x2 = 0 + -21.66666667

Combine like terms: 0 + -21.66666667 = -21.66666667
-10.66666667x + x2 = -21.66666667

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = -21.66666667 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = -21.66666667 + 28.44444446

Combine like terms: -21.66666667 + 28.44444446 = 6.77777779
28.44444446 + -10.66666667x + x2 = 6.77777779

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 6.77777779

Calculate the square root of the right side: 2.603416561

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 2.603416561 and -2.603416561.

Subproblem 1

x + -5.333333335 = 2.603416561 Simplifying x + -5.333333335 = 2.603416561 Reorder the terms: -5.333333335 + x = 2.603416561 Solving -5.333333335 + x = 2.603416561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 2.603416561 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 2.603416561 + 5.333333335 x = 2.603416561 + 5.333333335 Combine like terms: 2.603416561 + 5.333333335 = 7.936749896 x = 7.936749896 Simplifying x = 7.936749896

Subproblem 2

x + -5.333333335 = -2.603416561 Simplifying x + -5.333333335 = -2.603416561 Reorder the terms: -5.333333335 + x = -2.603416561 Solving -5.333333335 + x = -2.603416561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -2.603416561 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -2.603416561 + 5.333333335 x = -2.603416561 + 5.333333335 Combine like terms: -2.603416561 + 5.333333335 = 2.729916774 x = 2.729916774 Simplifying x = 2.729916774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.936749896, 2.729916774}

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