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Simplifying 5y + 2 = y2 + -12y + 4 Reorder the terms: 2 + 5y = y2 + -12y + 4 Reorder the terms: 2 + 5y = 4 + -12y + y2 Solving 2 + 5y = 4 + -12y + y2 Solving for variable 'y'. Reorder the terms: 2 + -4 + 5y + 12y + -1y2 = 4 + -12y + y2 + -4 + 12y + -1y2 Combine like terms: 2 + -4 = -2 -2 + 5y + 12y + -1y2 = 4 + -12y + y2 + -4 + 12y + -1y2 Combine like terms: 5y + 12y = 17y -2 + 17y + -1y2 = 4 + -12y + y2 + -4 + 12y + -1y2 Reorder the terms: -2 + 17y + -1y2 = 4 + -4 + -12y + 12y + y2 + -1y2 Combine like terms: 4 + -4 = 0 -2 + 17y + -1y2 = 0 + -12y + 12y + y2 + -1y2 -2 + 17y + -1y2 = -12y + 12y + y2 + -1y2 Combine like terms: -12y + 12y = 0 -2 + 17y + -1y2 = 0 + y2 + -1y2 -2 + 17y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -2 + 17y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -17y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -17y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -17y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -17y + y2 = 0 + -2 -17y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -17y + y2 = -2 The y term is -17y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17y + 72.25 + y2 = -2 + 72.25 Reorder the terms: 72.25 + -17y + y2 = -2 + 72.25 Combine like terms: -2 + 72.25 = 70.25 72.25 + -17y + y2 = 70.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (y + -8.5) equal to 8.381527307 and -8.381527307.Subproblem 1
y + -8.5 = 8.381527307 Simplifying y + -8.5 = 8.381527307 Reorder the terms: -8.5 + y = 8.381527307 Solving -8.5 + y = 8.381527307 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = 8.381527307 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 8.381527307 + 8.5 y = 8.381527307 + 8.5 Combine like terms: 8.381527307 + 8.5 = 16.881527307 y = 16.881527307 Simplifying y = 16.881527307Subproblem 2
y + -8.5 = -8.381527307 Simplifying y + -8.5 = -8.381527307 Reorder the terms: -8.5 + y = -8.381527307 Solving -8.5 + y = -8.381527307 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = -8.381527307 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -8.381527307 + 8.5 y = -8.381527307 + 8.5 Combine like terms: -8.381527307 + 8.5 = 0.118472693 y = 0.118472693 Simplifying y = 0.118472693Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.881527307, 0.118472693}
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