y^2-15y+18=0

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Solution for y^2-15y+18=0 equation:


Simplifying
y2 + -15y + 18 = 0

Reorder the terms:
18 + -15y + y2 = 0

Solving
18 + -15y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -15y + -18 + y2 = 0 + -18

Reorder the terms:
18 + -18 + -15y + y2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -15y + y2 = 0 + -18
-15y + y2 = 0 + -18

Combine like terms: 0 + -18 = -18
-15y + y2 = -18

The y term is -15y.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15y + 56.25 + y2 = -18 + 56.25

Reorder the terms:
56.25 + -15y + y2 = -18 + 56.25

Combine like terms: -18 + 56.25 = 38.25
56.25 + -15y + y2 = 38.25

Factor a perfect square on the left side:
(y + -7.5)(y + -7.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(y + -7.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

y + -7.5 = 6.184658438 Simplifying y + -7.5 = 6.184658438 Reorder the terms: -7.5 + y = 6.184658438 Solving -7.5 + y = 6.184658438 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 6.184658438 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 6.184658438 + 7.5 y = 6.184658438 + 7.5 Combine like terms: 6.184658438 + 7.5 = 13.684658438 y = 13.684658438 Simplifying y = 13.684658438

Subproblem 2

y + -7.5 = -6.184658438 Simplifying y + -7.5 = -6.184658438 Reorder the terms: -7.5 + y = -6.184658438 Solving -7.5 + y = -6.184658438 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -6.184658438 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -6.184658438 + 7.5 y = -6.184658438 + 7.5 Combine like terms: -6.184658438 + 7.5 = 1.315341562 y = 1.315341562 Simplifying y = 1.315341562

Solution

The solution to the problem is based on the solutions from the subproblems. y = {13.684658438, 1.315341562}

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