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Simplifying 17y + -1y2 + -5 = -57 + 2y2 Reorder the terms: -5 + 17y + -1y2 = -57 + 2y2 Solving -5 + 17y + -1y2 = -57 + 2y2 Solving for variable 'y'. Reorder the terms: -5 + 57 + 17y + -1y2 + -2y2 = -57 + 2y2 + 57 + -2y2 Combine like terms: -5 + 57 = 52 52 + 17y + -1y2 + -2y2 = -57 + 2y2 + 57 + -2y2 Combine like terms: -1y2 + -2y2 = -3y2 52 + 17y + -3y2 = -57 + 2y2 + 57 + -2y2 Reorder the terms: 52 + 17y + -3y2 = -57 + 57 + 2y2 + -2y2 Combine like terms: -57 + 57 = 0 52 + 17y + -3y2 = 0 + 2y2 + -2y2 52 + 17y + -3y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 52 + 17y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -17.33333333 + -5.666666667y + y2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + -5.666666667y + 17.33333333 + y2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + -5.666666667y + y2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + -5.666666667y + y2 = 0 + 17.33333333 -5.666666667y + y2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 -5.666666667y + y2 = 17.33333333 The y term is -5.666666667y. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667y + 8.027777782 + y2 = 17.33333333 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667y + y2 = 17.33333333 + 8.027777782 Combine like terms: 17.33333333 + 8.027777782 = 25.361111112 8.027777782 + -5.666666667y + y2 = 25.361111112 Factor a perfect square on the left side: (y + -2.833333334)(y + -2.833333334) = 25.361111112 Calculate the square root of the right side: 5.035981643 Break this problem into two subproblems by setting (y + -2.833333334) equal to 5.035981643 and -5.035981643.Subproblem 1
y + -2.833333334 = 5.035981643 Simplifying y + -2.833333334 = 5.035981643 Reorder the terms: -2.833333334 + y = 5.035981643 Solving -2.833333334 + y = 5.035981643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + y = 5.035981643 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + y = 5.035981643 + 2.833333334 y = 5.035981643 + 2.833333334 Combine like terms: 5.035981643 + 2.833333334 = 7.869314977 y = 7.869314977 Simplifying y = 7.869314977Subproblem 2
y + -2.833333334 = -5.035981643 Simplifying y + -2.833333334 = -5.035981643 Reorder the terms: -2.833333334 + y = -5.035981643 Solving -2.833333334 + y = -5.035981643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + y = -5.035981643 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + y = -5.035981643 + 2.833333334 y = -5.035981643 + 2.833333334 Combine like terms: -5.035981643 + 2.833333334 = -2.202648309 y = -2.202648309 Simplifying y = -2.202648309Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.869314977, -2.202648309}
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