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Simplifying 7y3 + -18y2 + 6y = 0 Reorder the terms: 6y + -18y2 + 7y3 = 0 Solving 6y + -18y2 + 7y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(6 + -18y + 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 '(6 + -18y + 7y2)' equal to zero and attempt to solve: Simplifying 6 + -18y + 7y2 = 0 Solving 6 + -18y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + -2.571428571y + y2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -2.571428571y + -0.8571428571 + y2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -2.571428571y + y2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -2.571428571y + y2 = 0 + -0.8571428571 -2.571428571y + y2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -2.571428571y + y2 = -0.8571428571 The y term is -2.571428571y. Take half its coefficient (-1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. -2.571428571y + 1.653061225 + y2 = -0.8571428571 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571y + y2 = -0.8571428571 + 1.653061225 Combine like terms: -0.8571428571 + 1.653061225 = 0.7959183679 1.653061225 + -2.571428571y + y2 = 0.7959183679 Factor a perfect square on the left side: (y + -1.285714286)(y + -1.285714286) = 0.7959183679 Calculate the square root of the right side: 0.892142572 Break this problem into two subproblems by setting (y + -1.285714286) equal to 0.892142572 and -0.892142572.Subproblem 1
y + -1.285714286 = 0.892142572 Simplifying y + -1.285714286 = 0.892142572 Reorder the terms: -1.285714286 + y = 0.892142572 Solving -1.285714286 + y = 0.892142572 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + y = 0.892142572 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + y = 0.892142572 + 1.285714286 y = 0.892142572 + 1.285714286 Combine like terms: 0.892142572 + 1.285714286 = 2.177856858 y = 2.177856858 Simplifying y = 2.177856858Subproblem 2
y + -1.285714286 = -0.892142572 Simplifying y + -1.285714286 = -0.892142572 Reorder the terms: -1.285714286 + y = -0.892142572 Solving -1.285714286 + y = -0.892142572 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + y = -0.892142572 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + y = -0.892142572 + 1.285714286 y = -0.892142572 + 1.285714286 Combine like terms: -0.892142572 + 1.285714286 = 0.393571714 y = 0.393571714 Simplifying y = 0.393571714Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.177856858, 0.393571714}Solution
y = {0, 2.177856858, 0.393571714}
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