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Simplifying -3y2 + -18y + 141 = 0 Reorder the terms: 141 + -18y + -3y2 = 0 Solving 141 + -18y + -3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(47 + -6y + -1y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(47 + -6y + -1y2)' equal to zero and attempt to solve: Simplifying 47 + -6y + -1y2 = 0 Solving 47 + -6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 6y + y2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 6y + 47 + y2 = 0 + 47 Reorder the terms: -47 + 47 + 6y + y2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 6y + y2 = 0 + 47 6y + y2 = 0 + 47 Combine like terms: 0 + 47 = 47 6y + y2 = 47 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 = 47 + 9 Reorder the terms: 9 + 6y + y2 = 47 + 9 Combine like terms: 47 + 9 = 56 9 + 6y + y2 = 56 Factor a perfect square on the left side: (y + 3)(y + 3) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (y + 3) equal to 7.483314774 and -7.483314774.Subproblem 1
y + 3 = 7.483314774 Simplifying y + 3 = 7.483314774 Reorder the terms: 3 + y = 7.483314774 Solving 3 + y = 7.483314774 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 = 7.483314774 + -3 Combine like terms: 3 + -3 = 0 0 + y = 7.483314774 + -3 y = 7.483314774 + -3 Combine like terms: 7.483314774 + -3 = 4.483314774 y = 4.483314774 Simplifying y = 4.483314774Subproblem 2
y + 3 = -7.483314774 Simplifying y + 3 = -7.483314774 Reorder the terms: 3 + y = -7.483314774 Solving 3 + y = -7.483314774 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 = -7.483314774 + -3 Combine like terms: 3 + -3 = 0 0 + y = -7.483314774 + -3 y = -7.483314774 + -3 Combine like terms: -7.483314774 + -3 = -10.483314774 y = -10.483314774 Simplifying y = -10.483314774Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.483314774, -10.483314774}Solution
y = {4.483314774, -10.483314774}
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