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Simplifying 7y3 + -20y2 + -37y = 0 Reorder the terms: -37y + -20y2 + 7y3 = 0 Solving -37y + -20y2 + 7y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-37 + -20y + 7y2) = 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 '(-37 + -20y + 7y2)' equal to zero and attempt to solve: Simplifying -37 + -20y + 7y2 = 0 Solving -37 + -20y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.285714286 + -2.857142857y + y2 = 0 Move the constant term to the right: Add '5.285714286' to each side of the equation. -5.285714286 + -2.857142857y + 5.285714286 + y2 = 0 + 5.285714286 Reorder the terms: -5.285714286 + 5.285714286 + -2.857142857y + y2 = 0 + 5.285714286 Combine like terms: -5.285714286 + 5.285714286 = 0.000000000 0.000000000 + -2.857142857y + y2 = 0 + 5.285714286 -2.857142857y + y2 = 0 + 5.285714286 Combine like terms: 0 + 5.285714286 = 5.285714286 -2.857142857y + y2 = 5.285714286 The y term is -2.857142857y. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857y + 2.040816328 + y2 = 5.285714286 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857y + y2 = 5.285714286 + 2.040816328 Combine like terms: 5.285714286 + 2.040816328 = 7.326530614 2.040816328 + -2.857142857y + y2 = 7.326530614 Factor a perfect square on the left side: (y + -1.428571429)(y + -1.428571429) = 7.326530614 Calculate the square root of the right side: 2.706756475 Break this problem into two subproblems by setting (y + -1.428571429) equal to 2.706756475 and -2.706756475.Subproblem 1
y + -1.428571429 = 2.706756475 Simplifying y + -1.428571429 = 2.706756475 Reorder the terms: -1.428571429 + y = 2.706756475 Solving -1.428571429 + y = 2.706756475 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + y = 2.706756475 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + y = 2.706756475 + 1.428571429 y = 2.706756475 + 1.428571429 Combine like terms: 2.706756475 + 1.428571429 = 4.135327904 y = 4.135327904 Simplifying y = 4.135327904Subproblem 2
y + -1.428571429 = -2.706756475 Simplifying y + -1.428571429 = -2.706756475 Reorder the terms: -1.428571429 + y = -2.706756475 Solving -1.428571429 + y = -2.706756475 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + y = -2.706756475 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + y = -2.706756475 + 1.428571429 y = -2.706756475 + 1.428571429 Combine like terms: -2.706756475 + 1.428571429 = -1.278185046 y = -1.278185046 Simplifying y = -1.278185046Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.135327904, -1.278185046}Solution
y = {0, 4.135327904, -1.278185046}
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