17y^2-46y-3=0

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Solution for 17y^2-46y-3=0 equation:


Simplifying
17y2 + -46y + -3 = 0

Reorder the terms:
-3 + -46y + 17y2 = 0

Solving
-3 + -46y + 17y2 = 0

Solving for variable 'y'.

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

Divide each side by '17'.
-0.1764705882 + -2.705882353y + y2 = 0

Move the constant term to the right:

Add '0.1764705882' to each side of the equation.
-0.1764705882 + -2.705882353y + 0.1764705882 + y2 = 0 + 0.1764705882

Reorder the terms:
-0.1764705882 + 0.1764705882 + -2.705882353y + y2 = 0 + 0.1764705882

Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000
0.0000000000 + -2.705882353y + y2 = 0 + 0.1764705882
-2.705882353y + y2 = 0 + 0.1764705882

Combine like terms: 0 + 0.1764705882 = 0.1764705882
-2.705882353y + y2 = 0.1764705882

The y term is -2.705882353y.  Take half its coefficient (-1.352941177).
Square it (1.830449828) and add it to both sides.

Add '1.830449828' to each side of the equation.
-2.705882353y + 1.830449828 + y2 = 0.1764705882 + 1.830449828

Reorder the terms:
1.830449828 + -2.705882353y + y2 = 0.1764705882 + 1.830449828

Combine like terms: 0.1764705882 + 1.830449828 = 2.0069204162
1.830449828 + -2.705882353y + y2 = 2.0069204162

Factor a perfect square on the left side:
(y + -1.352941177)(y + -1.352941177) = 2.0069204162

Calculate the square root of the right side: 1.416658186

Break this problem into two subproblems by setting 
(y + -1.352941177) equal to 1.416658186 and -1.416658186.

Subproblem 1

y + -1.352941177 = 1.416658186 Simplifying y + -1.352941177 = 1.416658186 Reorder the terms: -1.352941177 + y = 1.416658186 Solving -1.352941177 + y = 1.416658186 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.352941177' to each side of the equation. -1.352941177 + 1.352941177 + y = 1.416658186 + 1.352941177 Combine like terms: -1.352941177 + 1.352941177 = 0.000000000 0.000000000 + y = 1.416658186 + 1.352941177 y = 1.416658186 + 1.352941177 Combine like terms: 1.416658186 + 1.352941177 = 2.769599363 y = 2.769599363 Simplifying y = 2.769599363

Subproblem 2

y + -1.352941177 = -1.416658186 Simplifying y + -1.352941177 = -1.416658186 Reorder the terms: -1.352941177 + y = -1.416658186 Solving -1.352941177 + y = -1.416658186 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.352941177' to each side of the equation. -1.352941177 + 1.352941177 + y = -1.416658186 + 1.352941177 Combine like terms: -1.352941177 + 1.352941177 = 0.000000000 0.000000000 + y = -1.416658186 + 1.352941177 y = -1.416658186 + 1.352941177 Combine like terms: -1.416658186 + 1.352941177 = -0.063717009 y = -0.063717009 Simplifying y = -0.063717009

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.769599363, -0.063717009}

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