y^2-22.5y+112.5=0

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Solution for y^2-22.5y+112.5=0 equation:


Simplifying
y2 + -22.5y + 112.5 = 0

Reorder the terms:
112.5 + -22.5y + y2 = 0

Solving
112.5 + -22.5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-112.5' to each side of the equation.
112.5 + -22.5y + -112.5 + y2 = 0 + -112.5

Reorder the terms:
112.5 + -112.5 + -22.5y + y2 = 0 + -112.5

Combine like terms: 112.5 + -112.5 = 0.0
0.0 + -22.5y + y2 = 0 + -112.5
-22.5y + y2 = 0 + -112.5

Combine like terms: 0 + -112.5 = -112.5
-22.5y + y2 = -112.5

The y term is -22.5y.  Take half its coefficient (-11.25).
Square it (126.5625) and add it to both sides.

Add '126.5625' to each side of the equation.
-22.5y + 126.5625 + y2 = -112.5 + 126.5625

Reorder the terms:
126.5625 + -22.5y + y2 = -112.5 + 126.5625

Combine like terms: -112.5 + 126.5625 = 14.0625
126.5625 + -22.5y + y2 = 14.0625

Factor a perfect square on the left side:
(y + -11.25)(y + -11.25) = 14.0625

Calculate the square root of the right side: 3.75

Break this problem into two subproblems by setting 
(y + -11.25) equal to 3.75 and -3.75.

Subproblem 1

y + -11.25 = 3.75 Simplifying y + -11.25 = 3.75 Reorder the terms: -11.25 + y = 3.75 Solving -11.25 + y = 3.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + y = 3.75 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + y = 3.75 + 11.25 y = 3.75 + 11.25 Combine like terms: 3.75 + 11.25 = 15 y = 15 Simplifying y = 15

Subproblem 2

y + -11.25 = -3.75 Simplifying y + -11.25 = -3.75 Reorder the terms: -11.25 + y = -3.75 Solving -11.25 + y = -3.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + y = -3.75 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + y = -3.75 + 11.25 y = -3.75 + 11.25 Combine like terms: -3.75 + 11.25 = 7.5 y = 7.5 Simplifying y = 7.5

Solution

The solution to the problem is based on the solutions from the subproblems. y = {15, 7.5}

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