3x^2+60-32x=0

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Solution for 3x^2+60-32x=0 equation:


Simplifying
3x2 + 60 + -32x = 0

Reorder the terms:
60 + -32x + 3x2 = 0

Solving
60 + -32x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
20 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10.66666667x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10.66666667x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10.66666667x + x2 = 0 + -20
-10.66666667x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10.66666667x + x2 = -20

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 = -20 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = -20 + 28.44444446

Combine like terms: -20 + 28.44444446 = 8.44444446
28.44444446 + -10.66666667x + x2 = 8.44444446

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 8.44444446

Calculate the square root of the right side: 2.905932632

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 2.905932632 and -2.905932632.

Subproblem 1

x + -5.333333335 = 2.905932632 Simplifying x + -5.333333335 = 2.905932632 Reorder the terms: -5.333333335 + x = 2.905932632 Solving -5.333333335 + x = 2.905932632 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 = 2.905932632 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 2.905932632 + 5.333333335 x = 2.905932632 + 5.333333335 Combine like terms: 2.905932632 + 5.333333335 = 8.239265967 x = 8.239265967 Simplifying x = 8.239265967

Subproblem 2

x + -5.333333335 = -2.905932632 Simplifying x + -5.333333335 = -2.905932632 Reorder the terms: -5.333333335 + x = -2.905932632 Solving -5.333333335 + x = -2.905932632 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 = -2.905932632 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -2.905932632 + 5.333333335 x = -2.905932632 + 5.333333335 Combine like terms: -2.905932632 + 5.333333335 = 2.427400703 x = 2.427400703 Simplifying x = 2.427400703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.239265967, 2.427400703}

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