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Simplifying y3 + -16y2 + -63y = 0 Reorder the terms: -63y + -16y2 + y3 = 0 Solving -63y + -16y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-63 + -16y + y2) = 0Subproblem 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 '(-63 + -16y + y2)' equal to zero and attempt to solve: Simplifying -63 + -16y + y2 = 0 Solving -63 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -16y + 63 + y2 = 0 + 63 Reorder the terms: -63 + 63 + -16y + y2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -16y + y2 = 0 + 63 -16y + y2 = 0 + 63 Combine like terms: 0 + 63 = 63 -16y + y2 = 63 The y term is -16y. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16y + 64 + y2 = 63 + 64 Reorder the terms: 64 + -16y + y2 = 63 + 64 Combine like terms: 63 + 64 = 127 64 + -16y + y2 = 127 Factor a perfect square on the left side: (y + -8)(y + -8) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (y + -8) equal to 11.26942767 and -11.26942767.Subproblem 1
y + -8 = 11.26942767 Simplifying y + -8 = 11.26942767 Reorder the terms: -8 + y = 11.26942767 Solving -8 + y = 11.26942767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + y = 11.26942767 + 8 y = 11.26942767 + 8 Combine like terms: 11.26942767 + 8 = 19.26942767 y = 19.26942767 Simplifying y = 19.26942767Subproblem 2
y + -8 = -11.26942767 Simplifying y + -8 = -11.26942767 Reorder the terms: -8 + y = -11.26942767 Solving -8 + y = -11.26942767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -11.26942767 + 8 Combine like terms: -8 + 8 = 0 0 + y = -11.26942767 + 8 y = -11.26942767 + 8 Combine like terms: -11.26942767 + 8 = -3.26942767 y = -3.26942767 Simplifying y = -3.26942767Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.26942767, -3.26942767}Solution
y = {0, 19.26942767, -3.26942767}
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