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Simplifying 10y3 = 21y2 + -7y Reorder the terms: 10y3 = -7y + 21y2 Solving 10y3 = -7y + 21y2 Solving for variable 'y'. Reorder the terms: 7y + -21y2 + 10y3 = -7y + 21y2 + 7y + -21y2 Reorder the terms: 7y + -21y2 + 10y3 = -7y + 7y + 21y2 + -21y2 Combine like terms: -7y + 7y = 0 7y + -21y2 + 10y3 = 0 + 21y2 + -21y2 7y + -21y2 + 10y3 = 21y2 + -21y2 Combine like terms: 21y2 + -21y2 = 0 7y + -21y2 + 10y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(7 + -21y + 10y2) = 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 '(7 + -21y + 10y2)' equal to zero and attempt to solve: Simplifying 7 + -21y + 10y2 = 0 Solving 7 + -21y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.7 + -2.1y + y2 = 0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -2.1y + -0.7 + y2 = 0 + -0.7 Reorder the terms: 0.7 + -0.7 + -2.1y + y2 = 0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -2.1y + y2 = 0 + -0.7 -2.1y + y2 = 0 + -0.7 Combine like terms: 0 + -0.7 = -0.7 -2.1y + y2 = -0.7 The y term is -2.1y. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1y + 1.1025 + y2 = -0.7 + 1.1025 Reorder the terms: 1.1025 + -2.1y + y2 = -0.7 + 1.1025 Combine like terms: -0.7 + 1.1025 = 0.4025 1.1025 + -2.1y + y2 = 0.4025 Factor a perfect square on the left side: (y + -1.05)(y + -1.05) = 0.4025 Calculate the square root of the right side: 0.634428877 Break this problem into two subproblems by setting (y + -1.05) equal to 0.634428877 and -0.634428877.Subproblem 1
y + -1.05 = 0.634428877 Simplifying y + -1.05 = 0.634428877 Reorder the terms: -1.05 + y = 0.634428877 Solving -1.05 + y = 0.634428877 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + y = 0.634428877 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + y = 0.634428877 + 1.05 y = 0.634428877 + 1.05 Combine like terms: 0.634428877 + 1.05 = 1.684428877 y = 1.684428877 Simplifying y = 1.684428877Subproblem 2
y + -1.05 = -0.634428877 Simplifying y + -1.05 = -0.634428877 Reorder the terms: -1.05 + y = -0.634428877 Solving -1.05 + y = -0.634428877 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + y = -0.634428877 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + y = -0.634428877 + 1.05 y = -0.634428877 + 1.05 Combine like terms: -0.634428877 + 1.05 = 0.415571123 y = 0.415571123 Simplifying y = 0.415571123Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.684428877, 0.415571123}Solution
y = {0, 1.684428877, 0.415571123}
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