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Simplifying 3y2 + 18y + -1y + -24 = 0 Reorder the terms: -24 + 18y + -1y + 3y2 = 0 Combine like terms: 18y + -1y = 17y -24 + 17y + 3y2 = 0 Solving -24 + 17y + 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'. -8 + 5.666666667y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 5.666666667y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + 5.666666667y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5.666666667y + y2 = 0 + 8 5.666666667y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 5.666666667y + y2 = 8 The y term is 5.666666667y. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667y + 8.027777782 + y2 = 8 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667y + y2 = 8 + 8.027777782 Combine like terms: 8 + 8.027777782 = 16.027777782 8.027777782 + 5.666666667y + y2 = 16.027777782 Factor a perfect square on the left side: (y + 2.833333334)(y + 2.833333334) = 16.027777782 Calculate the square root of the right side: 4.003470717 Break this problem into two subproblems by setting (y + 2.833333334) equal to 4.003470717 and -4.003470717.Subproblem 1
y + 2.833333334 = 4.003470717 Simplifying y + 2.833333334 = 4.003470717 Reorder the terms: 2.833333334 + y = 4.003470717 Solving 2.833333334 + y = 4.003470717 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + y = 4.003470717 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + y = 4.003470717 + -2.833333334 y = 4.003470717 + -2.833333334 Combine like terms: 4.003470717 + -2.833333334 = 1.170137383 y = 1.170137383 Simplifying y = 1.170137383Subproblem 2
y + 2.833333334 = -4.003470717 Simplifying y + 2.833333334 = -4.003470717 Reorder the terms: 2.833333334 + y = -4.003470717 Solving 2.833333334 + y = -4.003470717 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + y = -4.003470717 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + y = -4.003470717 + -2.833333334 y = -4.003470717 + -2.833333334 Combine like terms: -4.003470717 + -2.833333334 = -6.836804051 y = -6.836804051 Simplifying y = -6.836804051Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.170137383, -6.836804051}
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