(9y^2-18y-4)-(-13y^2+3y+7)=

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Solution for (9y^2-18y-4)-(-13y^2+3y+7)= equation:


Simplifying
(9y2 + -18y + -4) + -1(-13y2 + 3y + 7) = 0

Reorder the terms:
(-4 + -18y + 9y2) + -1(-13y2 + 3y + 7) = 0

Remove parenthesis around (-4 + -18y + 9y2)
-4 + -18y + 9y2 + -1(-13y2 + 3y + 7) = 0

Reorder the terms:
-4 + -18y + 9y2 + -1(7 + 3y + -13y2) = 0
-4 + -18y + 9y2 + (7 * -1 + 3y * -1 + -13y2 * -1) = 0
-4 + -18y + 9y2 + (-7 + -3y + 13y2) = 0

Reorder the terms:
-4 + -7 + -18y + -3y + 9y2 + 13y2 = 0

Combine like terms: -4 + -7 = -11
-11 + -18y + -3y + 9y2 + 13y2 = 0

Combine like terms: -18y + -3y = -21y
-11 + -21y + 9y2 + 13y2 = 0

Combine like terms: 9y2 + 13y2 = 22y2
-11 + -21y + 22y2 = 0

Solving
-11 + -21y + 22y2 = 0

Solving for variable 'y'.

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

Divide each side by '22'.
-0.5 + -0.9545454545y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.9545454545y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.9545454545y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.9545454545y + y2 = 0 + 0.5
-0.9545454545y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.9545454545y + y2 = 0.5

The y term is -0.9545454545y.  Take half its coefficient (-0.4772727273).
Square it (0.2277892562) and add it to both sides.

Add '0.2277892562' to each side of the equation.
-0.9545454545y + 0.2277892562 + y2 = 0.5 + 0.2277892562

Reorder the terms:
0.2277892562 + -0.9545454545y + y2 = 0.5 + 0.2277892562

Combine like terms: 0.5 + 0.2277892562 = 0.7277892562
0.2277892562 + -0.9545454545y + y2 = 0.7277892562

Factor a perfect square on the left side:
(y + -0.4772727273)(y + -0.4772727273) = 0.7277892562

Calculate the square root of the right side: 0.853105654

Break this problem into two subproblems by setting 
(y + -0.4772727273) equal to 0.853105654 and -0.853105654.

Subproblem 1

y + -0.4772727273 = 0.853105654 Simplifying y + -0.4772727273 = 0.853105654 Reorder the terms: -0.4772727273 + y = 0.853105654 Solving -0.4772727273 + y = 0.853105654 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4772727273' to each side of the equation. -0.4772727273 + 0.4772727273 + y = 0.853105654 + 0.4772727273 Combine like terms: -0.4772727273 + 0.4772727273 = 0.0000000000 0.0000000000 + y = 0.853105654 + 0.4772727273 y = 0.853105654 + 0.4772727273 Combine like terms: 0.853105654 + 0.4772727273 = 1.3303783813 y = 1.3303783813 Simplifying y = 1.3303783813

Subproblem 2

y + -0.4772727273 = -0.853105654 Simplifying y + -0.4772727273 = -0.853105654 Reorder the terms: -0.4772727273 + y = -0.853105654 Solving -0.4772727273 + y = -0.853105654 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4772727273' to each side of the equation. -0.4772727273 + 0.4772727273 + y = -0.853105654 + 0.4772727273 Combine like terms: -0.4772727273 + 0.4772727273 = 0.0000000000 0.0000000000 + y = -0.853105654 + 0.4772727273 y = -0.853105654 + 0.4772727273 Combine like terms: -0.853105654 + 0.4772727273 = -0.3758329267 y = -0.3758329267 Simplifying y = -0.3758329267

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.3303783813, -0.3758329267}

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