4y^2-12y-9=0

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Solution for 4y^2-12y-9=0 equation:


Simplifying
4y2 + -12y + -9 = 0

Reorder the terms:
-9 + -12y + 4y2 = 0

Solving
-9 + -12y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
-2.25 + -3y + y2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -3y + 2.25 + y2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -3y + y2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -3y + y2 = 0 + 2.25
-3y + y2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-3y + y2 = 2.25

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 2.25 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 2.25 + 2.25

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + -3y + y2 = 4.5

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(y + -1.5) equal to 2.121320344 and -2.121320344.

Subproblem 1

y + -1.5 = 2.121320344 Simplifying y + -1.5 = 2.121320344 Reorder the terms: -1.5 + y = 2.121320344 Solving -1.5 + y = 2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 2.121320344 + 1.5 y = 2.121320344 + 1.5 Combine like terms: 2.121320344 + 1.5 = 3.621320344 y = 3.621320344 Simplifying y = 3.621320344

Subproblem 2

y + -1.5 = -2.121320344 Simplifying y + -1.5 = -2.121320344 Reorder the terms: -1.5 + y = -2.121320344 Solving -1.5 + y = -2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -2.121320344 + 1.5 y = -2.121320344 + 1.5 Combine like terms: -2.121320344 + 1.5 = -0.621320344 y = -0.621320344 Simplifying y = -0.621320344

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.621320344, -0.621320344}

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