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Simplifying 25y3 + -46y2 + 3y = 0 Reorder the terms: 3y + -46y2 + 25y3 = 0 Solving 3y + -46y2 + 25y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(3 + -46y + 25y2) = 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 '(3 + -46y + 25y2)' equal to zero and attempt to solve: Simplifying 3 + -46y + 25y2 = 0 Solving 3 + -46y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.12 + -1.84y + y2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -1.84y + -0.12 + y2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -1.84y + y2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -1.84y + y2 = 0 + -0.12 -1.84y + y2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -1.84y + y2 = -0.12 The y term is -1.84y. Take half its coefficient (-0.92). Square it (0.8464) and add it to both sides. Add '0.8464' to each side of the equation. -1.84y + 0.8464 + y2 = -0.12 + 0.8464 Reorder the terms: 0.8464 + -1.84y + y2 = -0.12 + 0.8464 Combine like terms: -0.12 + 0.8464 = 0.7264 0.8464 + -1.84y + y2 = 0.7264 Factor a perfect square on the left side: (y + -0.92)(y + -0.92) = 0.7264 Calculate the square root of the right side: 0.85229103 Break this problem into two subproblems by setting (y + -0.92) equal to 0.85229103 and -0.85229103.Subproblem 1
y + -0.92 = 0.85229103 Simplifying y + -0.92 = 0.85229103 Reorder the terms: -0.92 + y = 0.85229103 Solving -0.92 + y = 0.85229103 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + y = 0.85229103 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + y = 0.85229103 + 0.92 y = 0.85229103 + 0.92 Combine like terms: 0.85229103 + 0.92 = 1.77229103 y = 1.77229103 Simplifying y = 1.77229103Subproblem 2
y + -0.92 = -0.85229103 Simplifying y + -0.92 = -0.85229103 Reorder the terms: -0.92 + y = -0.85229103 Solving -0.92 + y = -0.85229103 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + y = -0.85229103 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + y = -0.85229103 + 0.92 y = -0.85229103 + 0.92 Combine like terms: -0.85229103 + 0.92 = 0.06770897 y = 0.06770897 Simplifying y = 0.06770897Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.77229103, 0.06770897}Solution
y = {0, 1.77229103, 0.06770897}
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