(3y^2+3y-8)-(-8y+3)=

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Solution for (3y^2+3y-8)-(-8y+3)= equation:


Simplifying
(3y2 + 3y + -8) + -1(-8y + 3) = 0

Reorder the terms:
(-8 + 3y + 3y2) + -1(-8y + 3) = 0

Remove parenthesis around (-8 + 3y + 3y2)
-8 + 3y + 3y2 + -1(-8y + 3) = 0

Reorder the terms:
-8 + 3y + 3y2 + -1(3 + -8y) = 0
-8 + 3y + 3y2 + (3 * -1 + -8y * -1) = 0
-8 + 3y + 3y2 + (-3 + 8y) = 0

Reorder the terms:
-8 + -3 + 3y + 8y + 3y2 = 0

Combine like terms: -8 + -3 = -11
-11 + 3y + 8y + 3y2 = 0

Combine like terms: 3y + 8y = 11y
-11 + 11y + 3y2 = 0

Solving
-11 + 11y + 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'.
-3.666666667 + 3.666666667y + y2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667y + 3.666666667 + y2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + 3.666666667y + y2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + 3.666666667y + y2 = 0 + 3.666666667
3.666666667y + y2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
3.666666667y + y2 = 3.666666667

The y term is 3.666666667y.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667y + 3.361111114 + y2 = 3.666666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667y + y2 = 3.666666667 + 3.361111114

Combine like terms: 3.666666667 + 3.361111114 = 7.027777781
3.361111114 + 3.666666667y + y2 = 7.027777781

Factor a perfect square on the left side:
(y + 1.833333334)(y + 1.833333334) = 7.027777781

Calculate the square root of the right side: 2.650995621

Break this problem into two subproblems by setting 
(y + 1.833333334) equal to 2.650995621 and -2.650995621.

Subproblem 1

y + 1.833333334 = 2.650995621 Simplifying y + 1.833333334 = 2.650995621 Reorder the terms: 1.833333334 + y = 2.650995621 Solving 1.833333334 + y = 2.650995621 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + y = 2.650995621 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + y = 2.650995621 + -1.833333334 y = 2.650995621 + -1.833333334 Combine like terms: 2.650995621 + -1.833333334 = 0.817662287 y = 0.817662287 Simplifying y = 0.817662287

Subproblem 2

y + 1.833333334 = -2.650995621 Simplifying y + 1.833333334 = -2.650995621 Reorder the terms: 1.833333334 + y = -2.650995621 Solving 1.833333334 + y = -2.650995621 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + y = -2.650995621 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + y = -2.650995621 + -1.833333334 y = -2.650995621 + -1.833333334 Combine like terms: -2.650995621 + -1.833333334 = -4.484328955 y = -4.484328955 Simplifying y = -4.484328955

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.817662287, -4.484328955}

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