y^2-25y-60=0

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Solution for y^2-25y-60=0 equation:


Simplifying
y2 + -25y + -60 = 0

Reorder the terms:
-60 + -25y + y2 = 0

Solving
-60 + -25y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -25y + 60 + y2 = 0 + 60

Reorder the terms:
-60 + 60 + -25y + y2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -25y + y2 = 0 + 60
-25y + y2 = 0 + 60

Combine like terms: 0 + 60 = 60
-25y + y2 = 60

The y term is -25y.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25y + 156.25 + y2 = 60 + 156.25

Reorder the terms:
156.25 + -25y + y2 = 60 + 156.25

Combine like terms: 60 + 156.25 = 216.25
156.25 + -25y + y2 = 216.25

Factor a perfect square on the left side:
(y + -12.5)(y + -12.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(y + -12.5) equal to 14.70544117 and -14.70544117.

Subproblem 1

y + -12.5 = 14.70544117 Simplifying y + -12.5 = 14.70544117 Reorder the terms: -12.5 + y = 14.70544117 Solving -12.5 + y = 14.70544117 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = 14.70544117 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = 14.70544117 + 12.5 y = 14.70544117 + 12.5 Combine like terms: 14.70544117 + 12.5 = 27.20544117 y = 27.20544117 Simplifying y = 27.20544117

Subproblem 2

y + -12.5 = -14.70544117 Simplifying y + -12.5 = -14.70544117 Reorder the terms: -12.5 + y = -14.70544117 Solving -12.5 + y = -14.70544117 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = -14.70544117 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = -14.70544117 + 12.5 y = -14.70544117 + 12.5 Combine like terms: -14.70544117 + 12.5 = -2.20544117 y = -2.20544117 Simplifying y = -2.20544117

Solution

The solution to the problem is based on the solutions from the subproblems. y = {27.20544117, -2.20544117}

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