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Simplifying 3y2 + -33y + 6 = 0 Reorder the terms: 6 + -33y + 3y2 = 0 Solving 6 + -33y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -11y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -11y + y2)' equal to zero and attempt to solve: Simplifying 2 + -11y + y2 = 0 Solving 2 + -11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -11y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -11y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11y + y2 = 0 + -2 -11y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -11y + y2 = -2 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -2 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -2 + 30.25 Combine like terms: -2 + 30.25 = 28.25 30.25 + -11y + y2 = 28.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (y + -5.5) equal to 5.315072906 and -5.315072906.Subproblem 1
y + -5.5 = 5.315072906 Simplifying y + -5.5 = 5.315072906 Reorder the terms: -5.5 + y = 5.315072906 Solving -5.5 + y = 5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 5.315072906 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 5.315072906 + 5.5 y = 5.315072906 + 5.5 Combine like terms: 5.315072906 + 5.5 = 10.815072906 y = 10.815072906 Simplifying y = 10.815072906Subproblem 2
y + -5.5 = -5.315072906 Simplifying y + -5.5 = -5.315072906 Reorder the terms: -5.5 + y = -5.315072906 Solving -5.5 + y = -5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -5.315072906 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -5.315072906 + 5.5 y = -5.315072906 + 5.5 Combine like terms: -5.315072906 + 5.5 = 0.184927094 y = 0.184927094 Simplifying y = 0.184927094Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.815072906, 0.184927094}Solution
y = {10.815072906, 0.184927094}
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