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Simplifying 3y2 = 18y + -4 Reorder the terms: 3y2 = -4 + 18y Solving 3y2 = -4 + 18y Solving for variable 'y'. Reorder the terms: 4 + -18y + 3y2 = -4 + 18y + 4 + -18y Reorder the terms: 4 + -18y + 3y2 = -4 + 4 + 18y + -18y Combine like terms: -4 + 4 = 0 4 + -18y + 3y2 = 0 + 18y + -18y 4 + -18y + 3y2 = 18y + -18y Combine like terms: 18y + -18y = 0 4 + -18y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -6y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -6y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -6y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -6y + y2 = 0 + -1.333333333 -6y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -6y + y2 = -1.333333333 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 = -1.333333333 + 9 Reorder the terms: 9 + -6y + y2 = -1.333333333 + 9 Combine like terms: -1.333333333 + 9 = 7.666666667 9 + -6y + y2 = 7.666666667 Factor a perfect square on the left side: (y + -3)(y + -3) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (y + -3) equal to 2.768874621 and -2.768874621.Subproblem 1
y + -3 = 2.768874621 Simplifying y + -3 = 2.768874621 Reorder the terms: -3 + y = 2.768874621 Solving -3 + y = 2.768874621 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 = 2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.768874621 + 3 y = 2.768874621 + 3 Combine like terms: 2.768874621 + 3 = 5.768874621 y = 5.768874621 Simplifying y = 5.768874621Subproblem 2
y + -3 = -2.768874621 Simplifying y + -3 = -2.768874621 Reorder the terms: -3 + y = -2.768874621 Solving -3 + y = -2.768874621 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 = -2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.768874621 + 3 y = -2.768874621 + 3 Combine like terms: -2.768874621 + 3 = 0.231125379 y = 0.231125379 Simplifying y = 0.231125379Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.768874621, 0.231125379}
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