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

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


Simplifying
(-4y2 + -5y) + (5y2 + y + -4) = 0

Reorder the terms:
(-5y + -4y2) + (5y2 + y + -4) = 0

Remove parenthesis around (-5y + -4y2)
-5y + -4y2 + (5y2 + y + -4) = 0

Reorder the terms:
-5y + -4y2 + (-4 + y + 5y2) = 0

Remove parenthesis around (-4 + y + 5y2)
-5y + -4y2 + -4 + y + 5y2 = 0

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

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

Combine like terms: -4y2 + 5y2 = 1y2
-4 + -4y + 1y2 = 0

Solving
-4 + -4y + 1y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

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

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

Combine like terms: 4 + 4 = 8
4 + -4y + y2 = 8

Factor a perfect square on the left side:
(y + -2)(y + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(y + -2) equal to 2.828427125 and -2.828427125.

Subproblem 1

y + -2 = 2.828427125 Simplifying y + -2 = 2.828427125 Reorder the terms: -2 + y = 2.828427125 Solving -2 + y = 2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.828427125 + 2 y = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 y = 4.828427125 Simplifying y = 4.828427125

Subproblem 2

y + -2 = -2.828427125 Simplifying y + -2 = -2.828427125 Reorder the terms: -2 + y = -2.828427125 Solving -2 + y = -2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.828427125 + 2 y = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 y = -0.828427125 Simplifying y = -0.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. y = {4.828427125, -0.828427125}

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