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Simplifying 6y2 + y + 53 = 5y2 + 19y + -17 Reorder the terms: 53 + y + 6y2 = 5y2 + 19y + -17 Reorder the terms: 53 + y + 6y2 = -17 + 19y + 5y2 Solving 53 + y + 6y2 = -17 + 19y + 5y2 Solving for variable 'y'. Reorder the terms: 53 + 17 + y + -19y + 6y2 + -5y2 = -17 + 19y + 5y2 + 17 + -19y + -5y2 Combine like terms: 53 + 17 = 70 70 + y + -19y + 6y2 + -5y2 = -17 + 19y + 5y2 + 17 + -19y + -5y2 Combine like terms: y + -19y = -18y 70 + -18y + 6y2 + -5y2 = -17 + 19y + 5y2 + 17 + -19y + -5y2 Combine like terms: 6y2 + -5y2 = 1y2 70 + -18y + 1y2 = -17 + 19y + 5y2 + 17 + -19y + -5y2 Reorder the terms: 70 + -18y + 1y2 = -17 + 17 + 19y + -19y + 5y2 + -5y2 Combine like terms: -17 + 17 = 0 70 + -18y + 1y2 = 0 + 19y + -19y + 5y2 + -5y2 70 + -18y + 1y2 = 19y + -19y + 5y2 + -5y2 Combine like terms: 19y + -19y = 0 70 + -18y + 1y2 = 0 + 5y2 + -5y2 70 + -18y + 1y2 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 70 + -18y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -18y + -70 + y2 = 0 + -70 Reorder the terms: 70 + -70 + -18y + y2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -18y + y2 = 0 + -70 -18y + y2 = 0 + -70 Combine like terms: 0 + -70 = -70 -18y + y2 = -70 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = -70 + 81 Reorder the terms: 81 + -18y + y2 = -70 + 81 Combine like terms: -70 + 81 = 11 81 + -18y + y2 = 11 Factor a perfect square on the left side: (y + -9)(y + -9) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (y + -9) equal to 3.31662479 and -3.31662479.Subproblem 1
y + -9 = 3.31662479 Simplifying y + -9 = 3.31662479 Reorder the terms: -9 + y = 3.31662479 Solving -9 + y = 3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 3.31662479 + 9 Combine like terms: -9 + 9 = 0 0 + y = 3.31662479 + 9 y = 3.31662479 + 9 Combine like terms: 3.31662479 + 9 = 12.31662479 y = 12.31662479 Simplifying y = 12.31662479Subproblem 2
y + -9 = -3.31662479 Simplifying y + -9 = -3.31662479 Reorder the terms: -9 + y = -3.31662479 Solving -9 + y = -3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -3.31662479 + 9 Combine like terms: -9 + 9 = 0 0 + y = -3.31662479 + 9 y = -3.31662479 + 9 Combine like terms: -3.31662479 + 9 = 5.68337521 y = 5.68337521 Simplifying y = 5.68337521Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.31662479, 5.68337521}
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