-4y^2+9y=-6

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Solution for -4y^2+9y=-6 equation:


Simplifying
-4y2 + 9y = -6

Reorder the terms:
9y + -4y2 = -6

Solving
9y + -4y2 = -6

Solving for variable 'y'.

Reorder the terms:
6 + 9y + -4y2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 9y + -4y2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.5 + -2.25y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2.25y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2.25y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2.25y + y2 = 0 + 1.5
-2.25y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2.25y + y2 = 1.5

The y term is -2.25y.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25y + 1.265625 + y2 = 1.5 + 1.265625

Reorder the terms:
1.265625 + -2.25y + y2 = 1.5 + 1.265625

Combine like terms: 1.5 + 1.265625 = 2.765625
1.265625 + -2.25y + y2 = 2.765625

Factor a perfect square on the left side:
(y + -1.125)(y + -1.125) = 2.765625

Calculate the square root of the right side: 1.663016837

Break this problem into two subproblems by setting 
(y + -1.125) equal to 1.663016837 and -1.663016837.

Subproblem 1

y + -1.125 = 1.663016837 Simplifying y + -1.125 = 1.663016837 Reorder the terms: -1.125 + y = 1.663016837 Solving -1.125 + y = 1.663016837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = 1.663016837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = 1.663016837 + 1.125 y = 1.663016837 + 1.125 Combine like terms: 1.663016837 + 1.125 = 2.788016837 y = 2.788016837 Simplifying y = 2.788016837

Subproblem 2

y + -1.125 = -1.663016837 Simplifying y + -1.125 = -1.663016837 Reorder the terms: -1.125 + y = -1.663016837 Solving -1.125 + y = -1.663016837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = -1.663016837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = -1.663016837 + 1.125 y = -1.663016837 + 1.125 Combine like terms: -1.663016837 + 1.125 = -0.538016837 y = -0.538016837 Simplifying y = -0.538016837

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.788016837, -0.538016837}

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