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Simplifying -49y3 + 45y2 + 91y = 0 Reorder the terms: 91y + 45y2 + -49y3 = 0 Solving 91y + 45y2 + -49y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(91 + 45y + -49y2) = 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 '(91 + 45y + -49y2)' equal to zero and attempt to solve: Simplifying 91 + 45y + -49y2 = 0 Solving 91 + 45y + -49y2 = 0 Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -1.857142857 + -0.9183673469y + y2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -0.9183673469y + 1.857142857 + y2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -0.9183673469y + y2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -0.9183673469y + y2 = 0 + 1.857142857 -0.9183673469y + y2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -0.9183673469y + y2 = 1.857142857 The y term is -0.9183673469y. Take half its coefficient (-0.4591836735). Square it (0.2108496460) and add it to both sides. Add '0.2108496460' to each side of the equation. -0.9183673469y + 0.2108496460 + y2 = 1.857142857 + 0.2108496460 Reorder the terms: 0.2108496460 + -0.9183673469y + y2 = 1.857142857 + 0.2108496460 Combine like terms: 1.857142857 + 0.2108496460 = 2.067992503 0.2108496460 + -0.9183673469y + y2 = 2.067992503 Factor a perfect square on the left side: (y + -0.4591836735)(y + -0.4591836735) = 2.067992503 Calculate the square root of the right side: 1.438051634 Break this problem into two subproblems by setting (y + -0.4591836735) equal to 1.438051634 and -1.438051634.Subproblem 1
y + -0.4591836735 = 1.438051634 Simplifying y + -0.4591836735 = 1.438051634 Reorder the terms: -0.4591836735 + y = 1.438051634 Solving -0.4591836735 + y = 1.438051634 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.4591836735 + y = 1.438051634 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + y = 1.438051634 + 0.4591836735 y = 1.438051634 + 0.4591836735 Combine like terms: 1.438051634 + 0.4591836735 = 1.8972353075 y = 1.8972353075 Simplifying y = 1.8972353075Subproblem 2
y + -0.4591836735 = -1.438051634 Simplifying y + -0.4591836735 = -1.438051634 Reorder the terms: -0.4591836735 + y = -1.438051634 Solving -0.4591836735 + y = -1.438051634 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.4591836735 + y = -1.438051634 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + y = -1.438051634 + 0.4591836735 y = -1.438051634 + 0.4591836735 Combine like terms: -1.438051634 + 0.4591836735 = -0.9788679605 y = -0.9788679605 Simplifying y = -0.9788679605Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.8972353075, -0.9788679605}Solution
y = {0, 1.8972353075, -0.9788679605}
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