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Simplifying 3y2 + -18y = 93 Reorder the terms: -18y + 3y2 = 93 Solving -18y + 3y2 = 93 Solving for variable 'y'. Reorder the terms: -93 + -18y + 3y2 = 93 + -93 Combine like terms: 93 + -93 = 0 -93 + -18y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-31 + -6y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-31 + -6y + y2)' equal to zero and attempt to solve: Simplifying -31 + -6y + y2 = 0 Solving -31 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -6y + 31 + y2 = 0 + 31 Reorder the terms: -31 + 31 + -6y + y2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -6y + y2 = 0 + 31 -6y + y2 = 0 + 31 Combine like terms: 0 + 31 = 31 -6y + y2 = 31 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 = 31 + 9 Reorder the terms: 9 + -6y + y2 = 31 + 9 Combine like terms: 31 + 9 = 40 9 + -6y + y2 = 40 Factor a perfect square on the left side: (y + -3)(y + -3) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (y + -3) equal to 6.32455532 and -6.32455532.Subproblem 1
y + -3 = 6.32455532 Simplifying y + -3 = 6.32455532 Reorder the terms: -3 + y = 6.32455532 Solving -3 + y = 6.32455532 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 = 6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + y = 6.32455532 + 3 y = 6.32455532 + 3 Combine like terms: 6.32455532 + 3 = 9.32455532 y = 9.32455532 Simplifying y = 9.32455532Subproblem 2
y + -3 = -6.32455532 Simplifying y + -3 = -6.32455532 Reorder the terms: -3 + y = -6.32455532 Solving -3 + y = -6.32455532 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 = -6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + y = -6.32455532 + 3 y = -6.32455532 + 3 Combine like terms: -6.32455532 + 3 = -3.32455532 y = -3.32455532 Simplifying y = -3.32455532Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.32455532, -3.32455532}Solution
y = {9.32455532, -3.32455532}
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