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Simplifying 8y3 + 64y2 + 8y = 0 Reorder the terms: 8y + 64y2 + 8y3 = 0 Solving 8y + 64y2 + 8y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '8y'. 8y(1 + 8y + y2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(1 + 8y + y2)' equal to zero and attempt to solve: Simplifying 1 + 8y + y2 = 0 Solving 1 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 8y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 8y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8y + y2 = 0 + -1 8y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 8y + y2 = -1 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = -1 + 16 Reorder the terms: 16 + 8y + y2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + 8y + y2 = 15 Factor a perfect square on the left side: (y + 4)(y + 4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (y + 4) equal to 3.872983346 and -3.872983346.Subproblem 1
y + 4 = 3.872983346 Simplifying y + 4 = 3.872983346 Reorder the terms: 4 + y = 3.872983346 Solving 4 + y = 3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + y = 3.872983346 + -4 y = 3.872983346 + -4 Combine like terms: 3.872983346 + -4 = -0.127016654 y = -0.127016654 Simplifying y = -0.127016654Subproblem 2
y + 4 = -3.872983346 Simplifying y + 4 = -3.872983346 Reorder the terms: 4 + y = -3.872983346 Solving 4 + y = -3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + y = -3.872983346 + -4 y = -3.872983346 + -4 Combine like terms: -3.872983346 + -4 = -7.872983346 y = -7.872983346 Simplifying y = -7.872983346Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.127016654, -7.872983346}Solution
y = {0, -0.127016654, -7.872983346}
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