16y^2-3y-16=0

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Solution for 16y^2-3y-16=0 equation:


Simplifying
16y2 + -3y + -16 = 0

Reorder the terms:
-16 + -3y + 16y2 = 0

Solving
-16 + -3y + 16y2 = 0

Solving for variable 'y'.

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

Divide each side by '16'.
-1 + -0.1875y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.1875y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.1875y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.1875y + y2 = 0 + 1
-0.1875y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.1875y + y2 = 1

The y term is -0.1875y.  Take half its coefficient (-0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
-0.1875y + 0.0087890625 + y2 = 1 + 0.0087890625

Reorder the terms:
0.0087890625 + -0.1875y + y2 = 1 + 0.0087890625

Combine like terms: 1 + 0.0087890625 = 1.0087890625
0.0087890625 + -0.1875y + y2 = 1.0087890625

Factor a perfect square on the left side:
(y + -0.09375)(y + -0.09375) = 1.0087890625

Calculate the square root of the right side: 1.004384918

Break this problem into two subproblems by setting 
(y + -0.09375) equal to 1.004384918 and -1.004384918.

Subproblem 1

y + -0.09375 = 1.004384918 Simplifying y + -0.09375 = 1.004384918 Reorder the terms: -0.09375 + y = 1.004384918 Solving -0.09375 + y = 1.004384918 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + y = 1.004384918 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + y = 1.004384918 + 0.09375 y = 1.004384918 + 0.09375 Combine like terms: 1.004384918 + 0.09375 = 1.098134918 y = 1.098134918 Simplifying y = 1.098134918

Subproblem 2

y + -0.09375 = -1.004384918 Simplifying y + -0.09375 = -1.004384918 Reorder the terms: -0.09375 + y = -1.004384918 Solving -0.09375 + y = -1.004384918 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + y = -1.004384918 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + y = -1.004384918 + 0.09375 y = -1.004384918 + 0.09375 Combine like terms: -1.004384918 + 0.09375 = -0.910634918 y = -0.910634918 Simplifying y = -0.910634918

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.098134918, -0.910634918}

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