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Simplifying 7y3 + -9y2 + -2y = 0 Reorder the terms: -2y + -9y2 + 7y3 = 0 Solving -2y + -9y2 + 7y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-2 + -9y + 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 '(-2 + -9y + 7y2)' equal to zero and attempt to solve: Simplifying -2 + -9y + 7y2 = 0 Solving -2 + -9y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -1.285714286y + y2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1.285714286y + 0.2857142857 + y2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1.285714286y + y2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1.285714286y + y2 = 0 + 0.2857142857 -1.285714286y + y2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1.285714286y + y2 = 0.2857142857 The y term is -1.285714286y. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286y + 0.4132653063 + y2 = 0.2857142857 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286y + y2 = 0.2857142857 + 0.4132653063 Combine like terms: 0.2857142857 + 0.4132653063 = 0.698979592 0.4132653063 + -1.285714286y + y2 = 0.698979592 Factor a perfect square on the left side: (y + -0.642857143)(y + -0.642857143) = 0.698979592 Calculate the square root of the right side: 0.836049994 Break this problem into two subproblems by setting (y + -0.642857143) equal to 0.836049994 and -0.836049994.Subproblem 1
y + -0.642857143 = 0.836049994 Simplifying y + -0.642857143 = 0.836049994 Reorder the terms: -0.642857143 + y = 0.836049994 Solving -0.642857143 + y = 0.836049994 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + y = 0.836049994 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + y = 0.836049994 + 0.642857143 y = 0.836049994 + 0.642857143 Combine like terms: 0.836049994 + 0.642857143 = 1.478907137 y = 1.478907137 Simplifying y = 1.478907137Subproblem 2
y + -0.642857143 = -0.836049994 Simplifying y + -0.642857143 = -0.836049994 Reorder the terms: -0.642857143 + y = -0.836049994 Solving -0.642857143 + y = -0.836049994 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + y = -0.836049994 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + y = -0.836049994 + 0.642857143 y = -0.836049994 + 0.642857143 Combine like terms: -0.836049994 + 0.642857143 = -0.193192851 y = -0.193192851 Simplifying y = -0.193192851Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.478907137, -0.193192851}Solution
y = {0, 1.478907137, -0.193192851}
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