y^2-13y+20=0

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Solution for y^2-13y+20=0 equation:


Simplifying
y2 + -13y + 20 = 0

Reorder the terms:
20 + -13y + y2 = 0

Solving
20 + -13y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -13y + -20 + y2 = 0 + -20

Reorder the terms:
20 + -20 + -13y + y2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -13y + y2 = 0 + -20
-13y + y2 = 0 + -20

Combine like terms: 0 + -20 = -20
-13y + y2 = -20

The y term is -13y.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13y + 42.25 + y2 = -20 + 42.25

Reorder the terms:
42.25 + -13y + y2 = -20 + 42.25

Combine like terms: -20 + 42.25 = 22.25
42.25 + -13y + y2 = 22.25

Factor a perfect square on the left side:
(y + -6.5)(y + -6.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(y + -6.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

y + -6.5 = 4.716990566 Simplifying y + -6.5 = 4.716990566 Reorder the terms: -6.5 + y = 4.716990566 Solving -6.5 + y = 4.716990566 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = 4.716990566 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 4.716990566 + 6.5 y = 4.716990566 + 6.5 Combine like terms: 4.716990566 + 6.5 = 11.216990566 y = 11.216990566 Simplifying y = 11.216990566

Subproblem 2

y + -6.5 = -4.716990566 Simplifying y + -6.5 = -4.716990566 Reorder the terms: -6.5 + y = -4.716990566 Solving -6.5 + y = -4.716990566 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = -4.716990566 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -4.716990566 + 6.5 y = -4.716990566 + 6.5 Combine like terms: -4.716990566 + 6.5 = 1.783009434 y = 1.783009434 Simplifying y = 1.783009434

Solution

The solution to the problem is based on the solutions from the subproblems. y = {11.216990566, 1.783009434}

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