y^2=-45+15y

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Solution for y^2=-45+15y equation:


Simplifying
y2 = -45 + 15y

Solving
y2 = -45 + 15y

Solving for variable 'y'.

Reorder the terms:
45 + -15y + y2 = -45 + 15y + 45 + -15y

Reorder the terms:
45 + -15y + y2 = -45 + 45 + 15y + -15y

Combine like terms: -45 + 45 = 0
45 + -15y + y2 = 0 + 15y + -15y
45 + -15y + y2 = 15y + -15y

Combine like terms: 15y + -15y = 0
45 + -15y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -15y + -45 + y2 = 0 + -45

Reorder the terms:
45 + -45 + -15y + y2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -15y + y2 = 0 + -45
-15y + y2 = 0 + -45

Combine like terms: 0 + -45 = -45
-15y + y2 = -45

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 = -45 + 56.25

Reorder the terms:
56.25 + -15y + y2 = -45 + 56.25

Combine like terms: -45 + 56.25 = 11.25
56.25 + -15y + y2 = 11.25

Factor a perfect square on the left side:
(y + -7.5)(y + -7.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(y + -7.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

y + -7.5 = 3.354101966 Simplifying y + -7.5 = 3.354101966 Reorder the terms: -7.5 + y = 3.354101966 Solving -7.5 + y = 3.354101966 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 = 3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 3.354101966 + 7.5 y = 3.354101966 + 7.5 Combine like terms: 3.354101966 + 7.5 = 10.854101966 y = 10.854101966 Simplifying y = 10.854101966

Subproblem 2

y + -7.5 = -3.354101966 Simplifying y + -7.5 = -3.354101966 Reorder the terms: -7.5 + y = -3.354101966 Solving -7.5 + y = -3.354101966 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 = -3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -3.354101966 + 7.5 y = -3.354101966 + 7.5 Combine like terms: -3.354101966 + 7.5 = 4.145898034 y = 4.145898034 Simplifying y = 4.145898034

Solution

The solution to the problem is based on the solutions from the subproblems. y = {10.854101966, 4.145898034}

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