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Simplifying 2y2 + 90y + 625 = 0 Reorder the terms: 625 + 90y + 2y2 = 0 Solving 625 + 90y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 312.5 + 45y + y2 = 0 Move the constant term to the right: Add '-312.5' to each side of the equation. 312.5 + 45y + -312.5 + y2 = 0 + -312.5 Reorder the terms: 312.5 + -312.5 + 45y + y2 = 0 + -312.5 Combine like terms: 312.5 + -312.5 = 0.0 0.0 + 45y + y2 = 0 + -312.5 45y + y2 = 0 + -312.5 Combine like terms: 0 + -312.5 = -312.5 45y + y2 = -312.5 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 = -312.5 + 506.25 Reorder the terms: 506.25 + 45y + y2 = -312.5 + 506.25 Combine like terms: -312.5 + 506.25 = 193.75 506.25 + 45y + y2 = 193.75 Factor a perfect square on the left side: (y + 22.5)(y + 22.5) = 193.75 Calculate the square root of the right side: 13.919410907 Break this problem into two subproblems by setting (y + 22.5) equal to 13.919410907 and -13.919410907.Subproblem 1
y + 22.5 = 13.919410907 Simplifying y + 22.5 = 13.919410907 Reorder the terms: 22.5 + y = 13.919410907 Solving 22.5 + y = 13.919410907 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 = 13.919410907 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + y = 13.919410907 + -22.5 y = 13.919410907 + -22.5 Combine like terms: 13.919410907 + -22.5 = -8.580589093 y = -8.580589093 Simplifying y = -8.580589093Subproblem 2
y + 22.5 = -13.919410907 Simplifying y + 22.5 = -13.919410907 Reorder the terms: 22.5 + y = -13.919410907 Solving 22.5 + y = -13.919410907 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 = -13.919410907 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + y = -13.919410907 + -22.5 y = -13.919410907 + -22.5 Combine like terms: -13.919410907 + -22.5 = -36.419410907 y = -36.419410907 Simplifying y = -36.419410907Solution
The solution to the problem is based on the solutions from the subproblems. y = {-8.580589093, -36.419410907}
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