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Simplifying 3y2 + y + -18 = 0 Reorder the terms: -18 + y + 3y2 = 0 Solving -18 + y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.3333333333y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 0.3333333333y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.3333333333y + y2 = 0 + 6 0.3333333333y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.3333333333y + y2 = 6 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333y + 0.25 + y2 = 6 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = 6 + 0.25 Combine like terms: 6 + 0.25 = 6.25 0.25 + 0.3333333333y + y2 = 6.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (y + 0.5) equal to 2.5 and -2.5.Subproblem 1
y + 0.5 = 2.5 Simplifying y + 0.5 = 2.5 Reorder the terms: 0.5 + y = 2.5 Solving 0.5 + y = 2.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.5 + -0.5 y = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 y = 2 Simplifying y = 2Subproblem 2
y + 0.5 = -2.5 Simplifying y + 0.5 = -2.5 Reorder the terms: 0.5 + y = -2.5 Solving 0.5 + y = -2.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.5 + -0.5 y = -2.5 + -0.5 Combine like terms: -2.5 + -0.5 = -3 y = -3 Simplifying y = -3Solution
The solution to the problem is based on the solutions from the subproblems. y = {2, -3}
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