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Simplifying 6y2 + -54y = -12 Reorder the terms: -54y + 6y2 = -12 Solving -54y + 6y2 = -12 Solving for variable 'y'. Reorder the terms: 12 + -54y + 6y2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -54y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(2 + -9y + y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + -9y + y2)' equal to zero and attempt to solve: Simplifying 2 + -9y + y2 = 0 Solving 2 + -9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -9y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -9y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9y + y2 = 0 + -2 -9y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -9y + y2 = -2 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = -2 + 20.25 Reorder the terms: 20.25 + -9y + y2 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + -9y + y2 = 18.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + -4.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + -4.5 = 4.272001873 Simplifying y + -4.5 = 4.272001873 Reorder the terms: -4.5 + y = 4.272001873 Solving -4.5 + y = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 4.272001873 + 4.5 y = 4.272001873 + 4.5 Combine like terms: 4.272001873 + 4.5 = 8.772001873 y = 8.772001873 Simplifying y = 8.772001873Subproblem 2
y + -4.5 = -4.272001873 Simplifying y + -4.5 = -4.272001873 Reorder the terms: -4.5 + y = -4.272001873 Solving -4.5 + y = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -4.272001873 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -4.272001873 + 4.5 y = -4.272001873 + 4.5 Combine like terms: -4.272001873 + 4.5 = 0.227998127 y = 0.227998127 Simplifying y = 0.227998127Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.772001873, 0.227998127}Solution
y = {8.772001873, 0.227998127}
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