9y^2+18y-12=16y

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Solution for 9y^2+18y-12=16y equation:


Simplifying
9y2 + 18y + -12 = 16y

Reorder the terms:
-12 + 18y + 9y2 = 16y

Solving
-12 + 18y + 9y2 = 16y

Solving for variable 'y'.

Reorder the terms:
-12 + 18y + -16y + 9y2 = 16y + -16y

Combine like terms: 18y + -16y = 2y
-12 + 2y + 9y2 = 16y + -16y

Combine like terms: 16y + -16y = 0
-12 + 2y + 9y2 = 0

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

Divide each side by '9'.
-1.333333333 + 0.2222222222y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 0.2222222222y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 0.2222222222y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 0.2222222222y + y2 = 0 + 1.333333333
0.2222222222y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
0.2222222222y + y2 = 1.333333333

The y term is 0.2222222222y.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222y + 0.01234567901 + y2 = 1.333333333 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222y + y2 = 1.333333333 + 0.01234567901

Combine like terms: 1.333333333 + 0.01234567901 = 1.34567901201
0.01234567901 + 0.2222222222y + y2 = 1.34567901201

Factor a perfect square on the left side:
(y + 0.1111111111)(y + 0.1111111111) = 1.34567901201

Calculate the square root of the right side: 1.160034056

Break this problem into two subproblems by setting 
(y + 0.1111111111) equal to 1.160034056 and -1.160034056.

Subproblem 1

y + 0.1111111111 = 1.160034056 Simplifying y + 0.1111111111 = 1.160034056 Reorder the terms: 0.1111111111 + y = 1.160034056 Solving 0.1111111111 + y = 1.160034056 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + y = 1.160034056 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + y = 1.160034056 + -0.1111111111 y = 1.160034056 + -0.1111111111 Combine like terms: 1.160034056 + -0.1111111111 = 1.0489229449 y = 1.0489229449 Simplifying y = 1.0489229449

Subproblem 2

y + 0.1111111111 = -1.160034056 Simplifying y + 0.1111111111 = -1.160034056 Reorder the terms: 0.1111111111 + y = -1.160034056 Solving 0.1111111111 + y = -1.160034056 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + y = -1.160034056 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + y = -1.160034056 + -0.1111111111 y = -1.160034056 + -0.1111111111 Combine like terms: -1.160034056 + -0.1111111111 = -1.2711451671 y = -1.2711451671 Simplifying y = -1.2711451671

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.0489229449, -1.2711451671}

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