-.75-y^2+3y-2y^2=

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Solution for -.75-y^2+3y-2y^2= equation:


Simplifying
-0.75 + -1y2 + 3y + -2y2 = 0

Reorder the terms:
-0.75 + 3y + -1y2 + -2y2 = 0

Combine like terms: -1y2 + -2y2 = -3y2
-0.75 + 3y + -3y2 = 0

Solving
-0.75 + 3y + -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'.
0.25 + -1y + y2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1y + -0.25 + y2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1y + y2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1y + y2 = 0 + -0.25
-1y + y2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1y + y2 = -0.25

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = -0.25 + 0.25

Reorder the terms:
0.25 + -1y + y2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1y + y2 = 0.00

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(y + -0.5) equal to 0.00 and 0.00.

Subproblem 1

y + -0.5 = 0.00 Simplifying y + -0.5 = 0.00 Reorder the terms: -0.5 + y = 0.00 Solving -0.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 0.00 + 0.5 y = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 y = 0.5 Simplifying y = 0.5

Subproblem 2

y + -0.5 = 0.00 Simplifying y + -0.5 = 0.00 Reorder the terms: -0.5 + y = 0.00 Solving -0.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 0.00 + 0.5 y = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 y = 0.5 Simplifying y = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.5, 0.5}

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