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Simplifying 112.5 + y2 + -45y = 0 Reorder the terms: 112.5 + -45y + y2 = 0 Solving 112.5 + -45y + 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 + -45y + -112.5 + y2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -45y + y2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -45y + y2 = 0 + -112.5 -45y + y2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -45y + y2 = -112.5 The y term is -45y. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45y + 506.25 + y2 = -112.5 + 506.25 Reorder the terms: 506.25 + -45y + y2 = -112.5 + 506.25 Combine like terms: -112.5 + 506.25 = 393.75 506.25 + -45y + y2 = 393.75 Factor a perfect square on the left side: (y + -22.5)(y + -22.5) = 393.75 Calculate the square root of the right side: 19.843134833 Break this problem into two subproblems by setting (y + -22.5) equal to 19.843134833 and -19.843134833.Subproblem 1
y + -22.5 = 19.843134833 Simplifying y + -22.5 = 19.843134833 Reorder the terms: -22.5 + y = 19.843134833 Solving -22.5 + y = 19.843134833 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + y = 19.843134833 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + y = 19.843134833 + 22.5 y = 19.843134833 + 22.5 Combine like terms: 19.843134833 + 22.5 = 42.343134833 y = 42.343134833 Simplifying y = 42.343134833Subproblem 2
y + -22.5 = -19.843134833 Simplifying y + -22.5 = -19.843134833 Reorder the terms: -22.5 + y = -19.843134833 Solving -22.5 + y = -19.843134833 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + y = -19.843134833 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + y = -19.843134833 + 22.5 y = -19.843134833 + 22.5 Combine like terms: -19.843134833 + 22.5 = 2.656865167 y = 2.656865167 Simplifying y = 2.656865167Solution
The solution to the problem is based on the solutions from the subproblems. y = {42.343134833, 2.656865167}
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