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Simplifying (3y2) + 3y + -54 = 0 Reorder the terms: -54 + 3y + (3y2) = 0 Solving -54 + 3y + (3y2) = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-18 + y + y2)' equal to zero and attempt to solve: Simplifying -18 + y + y2 = 0 Solving -18 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + y + y2 = 0 + 18 y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 y + y2 = 18 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 18 + 0.25 Reorder the terms: 0.25 + y + y2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + y + y2 = 18.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + 0.5 = 4.272001873 Simplifying y + 0.5 = 4.272001873 Reorder the terms: 0.5 + y = 4.272001873 Solving 0.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 4.272001873 + -0.5 y = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 y = 3.772001873 Simplifying y = 3.772001873Subproblem 2
y + 0.5 = -4.272001873 Simplifying y + 0.5 = -4.272001873 Reorder the terms: 0.5 + y = -4.272001873 Solving 0.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -4.272001873 + -0.5 y = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 y = -4.772001873 Simplifying y = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.772001873, -4.772001873}Solution
y = {3.772001873, -4.772001873}
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