-80-35y+3y^2=

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Solution for -80-35y+3y^2= equation:


Simplifying
-80 + -35y + 3y2 = 0

Solving
-80 + -35y + 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'.
-26.66666667 + -11.66666667y + y2 = 0

Move the constant term to the right:

Add '26.66666667' to each side of the equation.
-26.66666667 + -11.66666667y + 26.66666667 + y2 = 0 + 26.66666667

Reorder the terms:
-26.66666667 + 26.66666667 + -11.66666667y + y2 = 0 + 26.66666667

Combine like terms: -26.66666667 + 26.66666667 = 0.00000000
0.00000000 + -11.66666667y + y2 = 0 + 26.66666667
-11.66666667y + y2 = 0 + 26.66666667

Combine like terms: 0 + 26.66666667 = 26.66666667
-11.66666667y + y2 = 26.66666667

The y term is -11.66666667y.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667y + 34.02777780 + y2 = 26.66666667 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667y + y2 = 26.66666667 + 34.02777780

Combine like terms: 26.66666667 + 34.02777780 = 60.69444447
34.02777780 + -11.66666667y + y2 = 60.69444447

Factor a perfect square on the left side:
(y + -5.833333335)(y + -5.833333335) = 60.69444447

Calculate the square root of the right side: 7.79066393

Break this problem into two subproblems by setting 
(y + -5.833333335) equal to 7.79066393 and -7.79066393.

Subproblem 1

y + -5.833333335 = 7.79066393 Simplifying y + -5.833333335 = 7.79066393 Reorder the terms: -5.833333335 + y = 7.79066393 Solving -5.833333335 + y = 7.79066393 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + y = 7.79066393 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + y = 7.79066393 + 5.833333335 y = 7.79066393 + 5.833333335 Combine like terms: 7.79066393 + 5.833333335 = 13.623997265 y = 13.623997265 Simplifying y = 13.623997265

Subproblem 2

y + -5.833333335 = -7.79066393 Simplifying y + -5.833333335 = -7.79066393 Reorder the terms: -5.833333335 + y = -7.79066393 Solving -5.833333335 + y = -7.79066393 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + y = -7.79066393 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + y = -7.79066393 + 5.833333335 y = -7.79066393 + 5.833333335 Combine like terms: -7.79066393 + 5.833333335 = -1.957330595 y = -1.957330595 Simplifying y = -1.957330595

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.623997265, -1.957330595}

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