(4y^2+5y-2)-(9y+3)=

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Solution for (4y^2+5y-2)-(9y+3)= equation:


Simplifying
(4y2 + 5y + -2) + -1(9y + 3) = 0

Reorder the terms:
(-2 + 5y + 4y2) + -1(9y + 3) = 0

Remove parenthesis around (-2 + 5y + 4y2)
-2 + 5y + 4y2 + -1(9y + 3) = 0

Reorder the terms:
-2 + 5y + 4y2 + -1(3 + 9y) = 0
-2 + 5y + 4y2 + (3 * -1 + 9y * -1) = 0
-2 + 5y + 4y2 + (-3 + -9y) = 0

Reorder the terms:
-2 + -3 + 5y + -9y + 4y2 = 0

Combine like terms: -2 + -3 = -5
-5 + 5y + -9y + 4y2 = 0

Combine like terms: 5y + -9y = -4y
-5 + -4y + 4y2 = 0

Solving
-5 + -4y + 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'.
-1.25 + -1y + y2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1y + 1.25 + y2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1y + y2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1y + y2 = 0 + 1.25
-1y + y2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1y + y2 = 1.25

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 = 1.25 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
0.25 + -1y + y2 = 1.5

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(y + -0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

y + -0.5 = 1.224744871 Simplifying y + -0.5 = 1.224744871 Reorder the terms: -0.5 + y = 1.224744871 Solving -0.5 + y = 1.224744871 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 = 1.224744871 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.224744871 + 0.5 y = 1.224744871 + 0.5 Combine like terms: 1.224744871 + 0.5 = 1.724744871 y = 1.724744871 Simplifying y = 1.724744871

Subproblem 2

y + -0.5 = -1.224744871 Simplifying y + -0.5 = -1.224744871 Reorder the terms: -0.5 + y = -1.224744871 Solving -0.5 + y = -1.224744871 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 = -1.224744871 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.224744871 + 0.5 y = -1.224744871 + 0.5 Combine like terms: -1.224744871 + 0.5 = -0.724744871 y = -0.724744871 Simplifying y = -0.724744871

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.724744871, -0.724744871}

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