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Simplifying 3y2 + -30y = 48 Reorder the terms: -30y + 3y2 = 48 Solving -30y + 3y2 = 48 Solving for variable 'y'. Reorder the terms: -48 + -30y + 3y2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -30y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + -10y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + -10y + y2)' equal to zero and attempt to solve: Simplifying -16 + -10y + y2 = 0 Solving -16 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -10y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + -10y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -10y + y2 = 0 + 16 -10y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 -10y + y2 = 16 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 16 + 25 Reorder the terms: 25 + -10y + y2 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + -10y + y2 = 41 Factor a perfect square on the left side: (y + -5)(y + -5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (y + -5) equal to 6.403124237 and -6.403124237.Subproblem 1
y + -5 = 6.403124237 Simplifying y + -5 = 6.403124237 Reorder the terms: -5 + y = 6.403124237 Solving -5 + y = 6.403124237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 6.403124237 + 5 Combine like terms: -5 + 5 = 0 0 + y = 6.403124237 + 5 y = 6.403124237 + 5 Combine like terms: 6.403124237 + 5 = 11.403124237 y = 11.403124237 Simplifying y = 11.403124237Subproblem 2
y + -5 = -6.403124237 Simplifying y + -5 = -6.403124237 Reorder the terms: -5 + y = -6.403124237 Solving -5 + y = -6.403124237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -6.403124237 + 5 Combine like terms: -5 + 5 = 0 0 + y = -6.403124237 + 5 y = -6.403124237 + 5 Combine like terms: -6.403124237 + 5 = -1.403124237 y = -1.403124237 Simplifying y = -1.403124237Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.403124237, -1.403124237}Solution
y = {11.403124237, -1.403124237}
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