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Simplifying 0 = 3y2 + -18y + 17 Reorder the terms: 0 = 17 + -18y + 3y2 Solving 0 = 17 + -18y + 3y2 Solving for variable 'y'. Combine like terms: 0 + -17 = -17 -17 + 18y + -3y2 = 17 + -18y + 3y2 + -17 + 18y + -3y2 Reorder the terms: -17 + 18y + -3y2 = 17 + -17 + -18y + 18y + 3y2 + -3y2 Combine like terms: 17 + -17 = 0 -17 + 18y + -3y2 = 0 + -18y + 18y + 3y2 + -3y2 -17 + 18y + -3y2 = -18y + 18y + 3y2 + -3y2 Combine like terms: -18y + 18y = 0 -17 + 18y + -3y2 = 0 + 3y2 + -3y2 -17 + 18y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -17 + 18y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5.666666667 + -6y + y2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + -6y + -5.666666667 + y2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + -6y + y2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + -6y + y2 = 0 + -5.666666667 -6y + y2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 -6y + y2 = -5.666666667 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -5.666666667 + 9 Reorder the terms: 9 + -6y + y2 = -5.666666667 + 9 Combine like terms: -5.666666667 + 9 = 3.333333333 9 + -6y + y2 = 3.333333333 Factor a perfect square on the left side: (y + -3)(y + -3) = 3.333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (y + -3) equal to 1.825741858 and -1.825741858.Subproblem 1
y + -3 = 1.825741858 Simplifying y + -3 = 1.825741858 Reorder the terms: -3 + y = 1.825741858 Solving -3 + y = 1.825741858 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 1.825741858 + 3 Combine like terms: -3 + 3 = 0 0 + y = 1.825741858 + 3 y = 1.825741858 + 3 Combine like terms: 1.825741858 + 3 = 4.825741858 y = 4.825741858 Simplifying y = 4.825741858Subproblem 2
y + -3 = -1.825741858 Simplifying y + -3 = -1.825741858 Reorder the terms: -3 + y = -1.825741858 Solving -3 + y = -1.825741858 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -1.825741858 + 3 Combine like terms: -3 + 3 = 0 0 + y = -1.825741858 + 3 y = -1.825741858 + 3 Combine like terms: -1.825741858 + 3 = 1.174258142 y = 1.174258142 Simplifying y = 1.174258142Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.825741858, 1.174258142}
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