-2y^2+3y+8=0

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Solution for -2y^2+3y+8=0 equation:


Simplifying
-2y2 + 3y + 8 = 0

Reorder the terms:
8 + 3y + -2y2 = 0

Solving
8 + 3y + -2y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4 + -1.5y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1.5y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + -1.5y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1.5y + y2 = 0 + 4
-1.5y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1.5y + y2 = 4

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 4 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = 4 + 0.5625

Combine like terms: 4 + 0.5625 = 4.5625
0.5625 + -1.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + -0.75) equal to 2.136000936 and -2.136000936.

Subproblem 1

y + -0.75 = 2.136000936 Simplifying y + -0.75 = 2.136000936 Reorder the terms: -0.75 + y = 2.136000936 Solving -0.75 + y = 2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 2.136000936 + 0.75 y = 2.136000936 + 0.75 Combine like terms: 2.136000936 + 0.75 = 2.886000936 y = 2.886000936 Simplifying y = 2.886000936

Subproblem 2

y + -0.75 = -2.136000936 Simplifying y + -0.75 = -2.136000936 Reorder the terms: -0.75 + y = -2.136000936 Solving -0.75 + y = -2.136000936 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -2.136000936 + 0.75 y = -2.136000936 + 0.75 Combine like terms: -2.136000936 + 0.75 = -1.386000936 y = -1.386000936 Simplifying y = -1.386000936

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.886000936, -1.386000936}

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