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Simplifying 3y2 + -11y = 30 Reorder the terms: -11y + 3y2 = 30 Solving -11y + 3y2 = 30 Solving for variable 'y'. Reorder the terms: -30 + -11y + 3y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -11y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + -3.666666667y + y2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -3.666666667y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + -3.666666667y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3.666666667y + y2 = 0 + 10 -3.666666667y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 -3.666666667y + y2 = 10 The y term is -3.666666667y. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667y + 3.361111114 + y2 = 10 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667y + y2 = 10 + 3.361111114 Combine like terms: 10 + 3.361111114 = 13.361111114 3.361111114 + -3.666666667y + y2 = 13.361111114 Factor a perfect square on the left side: (y + -1.833333334)(y + -1.833333334) = 13.361111114 Calculate the square root of the right side: 3.655285367 Break this problem into two subproblems by setting (y + -1.833333334) equal to 3.655285367 and -3.655285367.Subproblem 1
y + -1.833333334 = 3.655285367 Simplifying y + -1.833333334 = 3.655285367 Reorder the terms: -1.833333334 + y = 3.655285367 Solving -1.833333334 + y = 3.655285367 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + y = 3.655285367 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + y = 3.655285367 + 1.833333334 y = 3.655285367 + 1.833333334 Combine like terms: 3.655285367 + 1.833333334 = 5.488618701 y = 5.488618701 Simplifying y = 5.488618701Subproblem 2
y + -1.833333334 = -3.655285367 Simplifying y + -1.833333334 = -3.655285367 Reorder the terms: -1.833333334 + y = -3.655285367 Solving -1.833333334 + y = -3.655285367 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + y = -3.655285367 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + y = -3.655285367 + 1.833333334 y = -3.655285367 + 1.833333334 Combine like terms: -3.655285367 + 1.833333334 = -1.821952033 y = -1.821952033 Simplifying y = -1.821952033Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.488618701, -1.821952033}
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