Y^2-17Y-72=0

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Solution for Y^2-17Y-72=0 equation:


Simplifying
Y2 + -17Y + -72 = 0

Reorder the terms:
-72 + -17Y + Y2 = 0

Solving
-72 + -17Y + Y2 = 0

Solving for variable 'Y'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -17Y + 72 + Y2 = 0 + 72

Reorder the terms:
-72 + 72 + -17Y + Y2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -17Y + Y2 = 0 + 72
-17Y + Y2 = 0 + 72

Combine like terms: 0 + 72 = 72
-17Y + Y2 = 72

The Y term is -17Y.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17Y + 72.25 + Y2 = 72 + 72.25

Reorder the terms:
72.25 + -17Y + Y2 = 72 + 72.25

Combine like terms: 72 + 72.25 = 144.25
72.25 + -17Y + Y2 = 144.25

Factor a perfect square on the left side:
(Y + -8.5)(Y + -8.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(Y + -8.5) equal to 12.010412149 and -12.010412149.

Subproblem 1

Y + -8.5 = 12.010412149 Simplifying Y + -8.5 = 12.010412149 Reorder the terms: -8.5 + Y = 12.010412149 Solving -8.5 + Y = 12.010412149 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + Y = 12.010412149 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + Y = 12.010412149 + 8.5 Y = 12.010412149 + 8.5 Combine like terms: 12.010412149 + 8.5 = 20.510412149 Y = 20.510412149 Simplifying Y = 20.510412149

Subproblem 2

Y + -8.5 = -12.010412149 Simplifying Y + -8.5 = -12.010412149 Reorder the terms: -8.5 + Y = -12.010412149 Solving -8.5 + Y = -12.010412149 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + Y = -12.010412149 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + Y = -12.010412149 + 8.5 Y = -12.010412149 + 8.5 Combine like terms: -12.010412149 + 8.5 = -3.510412149 Y = -3.510412149 Simplifying Y = -3.510412149

Solution

The solution to the problem is based on the solutions from the subproblems. Y = {20.510412149, -3.510412149}

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