3y^2-20y-12=

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Solution for 3y^2-20y-12= equation:


Simplifying
3y2 + -20y + -12 = 0

Reorder the terms:
-12 + -20y + 3y2 = 0

Solving
-12 + -20y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-4 + -6.666666667y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6.666666667y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -6.666666667y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6.666666667y + y2 = 0 + 4
-6.666666667y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6.666666667y + y2 = 4

The y term is -6.666666667y.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667y + 11.11111112 + y2 = 4 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667y + y2 = 4 + 11.11111112

Combine like terms: 4 + 11.11111112 = 15.11111112
11.11111112 + -6.666666667y + y2 = 15.11111112

Factor a perfect square on the left side:
(y + -3.333333334)(y + -3.333333334) = 15.11111112

Calculate the square root of the right side: 3.887301264

Break this problem into two subproblems by setting 
(y + -3.333333334) equal to 3.887301264 and -3.887301264.

Subproblem 1

y + -3.333333334 = 3.887301264 Simplifying y + -3.333333334 = 3.887301264 Reorder the terms: -3.333333334 + y = 3.887301264 Solving -3.333333334 + y = 3.887301264 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + y = 3.887301264 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + y = 3.887301264 + 3.333333334 y = 3.887301264 + 3.333333334 Combine like terms: 3.887301264 + 3.333333334 = 7.220634598 y = 7.220634598 Simplifying y = 7.220634598

Subproblem 2

y + -3.333333334 = -3.887301264 Simplifying y + -3.333333334 = -3.887301264 Reorder the terms: -3.333333334 + y = -3.887301264 Solving -3.333333334 + y = -3.887301264 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + y = -3.887301264 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + y = -3.887301264 + 3.333333334 y = -3.887301264 + 3.333333334 Combine like terms: -3.887301264 + 3.333333334 = -0.55396793 y = -0.55396793 Simplifying y = -0.55396793

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.220634598, -0.55396793}

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