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Simplifying y4 + -16y3 + 74y2 = 0 Reorder the terms: 74y2 + -16y3 + y4 = 0 Solving 74y2 + -16y3 + y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(74 + -16y + y2) = 0Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(74 + -16y + y2)' equal to zero and attempt to solve: Simplifying 74 + -16y + y2 = 0 Solving 74 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-74' to each side of the equation. 74 + -16y + -74 + y2 = 0 + -74 Reorder the terms: 74 + -74 + -16y + y2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + -16y + y2 = 0 + -74 -16y + y2 = 0 + -74 Combine like terms: 0 + -74 = -74 -16y + y2 = -74 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 = -74 + 64 Reorder the terms: 64 + -16y + y2 = -74 + 64 Combine like terms: -74 + 64 = -10 64 + -16y + y2 = -10 Factor a perfect square on the left side: (y + -8)(y + -8) = -10 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
y = {0}
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