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Simplifying 5y3 + -39y2 + -38y = 0 Reorder the terms: -38y + -39y2 + 5y3 = 0 Solving -38y + -39y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-38 + -39y + 5y2) = 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 '(-38 + -39y + 5y2)' equal to zero and attempt to solve: Simplifying -38 + -39y + 5y2 = 0 Solving -38 + -39y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + -7.8y + y2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -7.8y + 7.6 + y2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -7.8y + y2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -7.8y + y2 = 0 + 7.6 -7.8y + y2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -7.8y + y2 = 7.6 The y term is -7.8y. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8y + 15.21 + y2 = 7.6 + 15.21 Reorder the terms: 15.21 + -7.8y + y2 = 7.6 + 15.21 Combine like terms: 7.6 + 15.21 = 22.81 15.21 + -7.8y + y2 = 22.81 Factor a perfect square on the left side: (y + -3.9)(y + -3.9) = 22.81 Calculate the square root of the right side: 4.775981575 Break this problem into two subproblems by setting (y + -3.9) equal to 4.775981575 and -4.775981575.Subproblem 1
y + -3.9 = 4.775981575 Simplifying y + -3.9 = 4.775981575 Reorder the terms: -3.9 + y = 4.775981575 Solving -3.9 + y = 4.775981575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + y = 4.775981575 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + y = 4.775981575 + 3.9 y = 4.775981575 + 3.9 Combine like terms: 4.775981575 + 3.9 = 8.675981575 y = 8.675981575 Simplifying y = 8.675981575Subproblem 2
y + -3.9 = -4.775981575 Simplifying y + -3.9 = -4.775981575 Reorder the terms: -3.9 + y = -4.775981575 Solving -3.9 + y = -4.775981575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + y = -4.775981575 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + y = -4.775981575 + 3.9 y = -4.775981575 + 3.9 Combine like terms: -4.775981575 + 3.9 = -0.875981575 y = -0.875981575 Simplifying y = -0.875981575Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.675981575, -0.875981575}Solution
y = {0, 8.675981575, -0.875981575}
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