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Simplifying 0 = y2 + -10y + -455 Reorder the terms: 0 = -455 + -10y + y2 Solving 0 = -455 + -10y + y2 Solving for variable 'y'. Combine like terms: 0 + 455 = 455 455 + 10y + -1y2 = -455 + -10y + y2 + 455 + 10y + -1y2 Reorder the terms: 455 + 10y + -1y2 = -455 + 455 + -10y + 10y + y2 + -1y2 Combine like terms: -455 + 455 = 0 455 + 10y + -1y2 = 0 + -10y + 10y + y2 + -1y2 455 + 10y + -1y2 = -10y + 10y + y2 + -1y2 Combine like terms: -10y + 10y = 0 455 + 10y + -1y2 = 0 + y2 + -1y2 455 + 10y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 455 + 10y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -455 + -10y + y2 = 0 Move the constant term to the right: Add '455' to each side of the equation. -455 + -10y + 455 + y2 = 0 + 455 Reorder the terms: -455 + 455 + -10y + y2 = 0 + 455 Combine like terms: -455 + 455 = 0 0 + -10y + y2 = 0 + 455 -10y + y2 = 0 + 455 Combine like terms: 0 + 455 = 455 -10y + y2 = 455 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 455 + 25 Reorder the terms: 25 + -10y + y2 = 455 + 25 Combine like terms: 455 + 25 = 480 25 + -10y + y2 = 480 Factor a perfect square on the left side: (y + -5)(y + -5) = 480 Calculate the square root of the right side: 21.9089023 Break this problem into two subproblems by setting (y + -5) equal to 21.9089023 and -21.9089023.Subproblem 1
y + -5 = 21.9089023 Simplifying y + -5 = 21.9089023 Reorder the terms: -5 + y = 21.9089023 Solving -5 + y = 21.9089023 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 21.9089023 + 5 Combine like terms: -5 + 5 = 0 0 + y = 21.9089023 + 5 y = 21.9089023 + 5 Combine like terms: 21.9089023 + 5 = 26.9089023 y = 26.9089023 Simplifying y = 26.9089023Subproblem 2
y + -5 = -21.9089023 Simplifying y + -5 = -21.9089023 Reorder the terms: -5 + y = -21.9089023 Solving -5 + y = -21.9089023 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -21.9089023 + 5 Combine like terms: -5 + 5 = 0 0 + y = -21.9089023 + 5 y = -21.9089023 + 5 Combine like terms: -21.9089023 + 5 = -16.9089023 y = -16.9089023 Simplifying y = -16.9089023Solution
The solution to the problem is based on the solutions from the subproblems. y = {26.9089023, -16.9089023}
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