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Simplifying 4y3 + y2 + -21y = 0 Reorder the terms: -21y + y2 + 4y3 = 0 Solving -21y + y2 + 4y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-21 + y + 4y2) = 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 '(-21 + y + 4y2)' equal to zero and attempt to solve: Simplifying -21 + y + 4y2 = 0 Solving -21 + y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 0.25y + y2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 0.25y + 5.25 + y2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 0.25y + y2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 0.25y + y2 = 0 + 5.25 0.25y + y2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 0.25y + y2 = 5.25 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25y + 0.25 + y2 = 5.25 + 0.25 Reorder the terms: 0.25 + 0.25y + y2 = 5.25 + 0.25 Combine like terms: 5.25 + 0.25 = 5.5 0.25 + 0.25y + y2 = 5.5 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (y + 0.5) equal to 2.34520788 and -2.34520788.Subproblem 1
y + 0.5 = 2.34520788 Simplifying y + 0.5 = 2.34520788 Reorder the terms: 0.5 + y = 2.34520788 Solving 0.5 + y = 2.34520788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 2.34520788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.34520788 + -0.5 y = 2.34520788 + -0.5 Combine like terms: 2.34520788 + -0.5 = 1.84520788 y = 1.84520788 Simplifying y = 1.84520788Subproblem 2
y + 0.5 = -2.34520788 Simplifying y + 0.5 = -2.34520788 Reorder the terms: 0.5 + y = -2.34520788 Solving 0.5 + y = -2.34520788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -2.34520788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.34520788 + -0.5 y = -2.34520788 + -0.5 Combine like terms: -2.34520788 + -0.5 = -2.84520788 y = -2.84520788 Simplifying y = -2.84520788Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.84520788, -2.84520788}Solution
y = {0, 1.84520788, -2.84520788}
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