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Simplifying 9y2 + -15y = y + 9 Reorder the terms: -15y + 9y2 = y + 9 Reorder the terms: -15y + 9y2 = 9 + y Solving -15y + 9y2 = 9 + y Solving for variable 'y'. Reorder the terms: -9 + -15y + -1y + 9y2 = 9 + y + -9 + -1y Combine like terms: -15y + -1y = -16y -9 + -16y + 9y2 = 9 + y + -9 + -1y Reorder the terms: -9 + -16y + 9y2 = 9 + -9 + y + -1y Combine like terms: 9 + -9 = 0 -9 + -16y + 9y2 = 0 + y + -1y -9 + -16y + 9y2 = y + -1y Combine like terms: y + -1y = 0 -9 + -16y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1 + -1.777777778y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.777777778y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -1.777777778y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.777777778y + y2 = 0 + 1 -1.777777778y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.777777778y + y2 = 1 The y term is -1.777777778y. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778y + 0.7901234570 + y2 = 1 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778y + y2 = 1 + 0.7901234570 Combine like terms: 1 + 0.7901234570 = 1.790123457 0.7901234570 + -1.777777778y + y2 = 1.790123457 Factor a perfect square on the left side: (y + -0.888888889)(y + -0.888888889) = 1.790123457 Calculate the square root of the right side: 1.337954953 Break this problem into two subproblems by setting (y + -0.888888889) equal to 1.337954953 and -1.337954953.Subproblem 1
y + -0.888888889 = 1.337954953 Simplifying y + -0.888888889 = 1.337954953 Reorder the terms: -0.888888889 + y = 1.337954953 Solving -0.888888889 + y = 1.337954953 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + y = 1.337954953 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + y = 1.337954953 + 0.888888889 y = 1.337954953 + 0.888888889 Combine like terms: 1.337954953 + 0.888888889 = 2.226843842 y = 2.226843842 Simplifying y = 2.226843842Subproblem 2
y + -0.888888889 = -1.337954953 Simplifying y + -0.888888889 = -1.337954953 Reorder the terms: -0.888888889 + y = -1.337954953 Solving -0.888888889 + y = -1.337954953 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + y = -1.337954953 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + y = -1.337954953 + 0.888888889 y = -1.337954953 + 0.888888889 Combine like terms: -1.337954953 + 0.888888889 = -0.449066064 y = -0.449066064 Simplifying y = -0.449066064Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.226843842, -0.449066064}
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