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Simplifying 25y3 + -166y2 + -70y = 0 Reorder the terms: -70y + -166y2 + 25y3 = 0 Solving -70y + -166y2 + 25y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-70 + -166y + 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 '(-70 + -166y + 25y2)' equal to zero and attempt to solve: Simplifying -70 + -166y + 25y2 = 0 Solving -70 + -166y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.8 + -6.64y + y2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -6.64y + 2.8 + y2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -6.64y + y2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -6.64y + y2 = 0 + 2.8 -6.64y + y2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -6.64y + y2 = 2.8 The y term is -6.64y. Take half its coefficient (-3.32). Square it (11.0224) and add it to both sides. Add '11.0224' to each side of the equation. -6.64y + 11.0224 + y2 = 2.8 + 11.0224 Reorder the terms: 11.0224 + -6.64y + y2 = 2.8 + 11.0224 Combine like terms: 2.8 + 11.0224 = 13.8224 11.0224 + -6.64y + y2 = 13.8224 Factor a perfect square on the left side: (y + -3.32)(y + -3.32) = 13.8224 Calculate the square root of the right side: 3.71784884 Break this problem into two subproblems by setting (y + -3.32) equal to 3.71784884 and -3.71784884.Subproblem 1
y + -3.32 = 3.71784884 Simplifying y + -3.32 = 3.71784884 Reorder the terms: -3.32 + y = 3.71784884 Solving -3.32 + y = 3.71784884 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.32' to each side of the equation. -3.32 + 3.32 + y = 3.71784884 + 3.32 Combine like terms: -3.32 + 3.32 = 0.00 0.00 + y = 3.71784884 + 3.32 y = 3.71784884 + 3.32 Combine like terms: 3.71784884 + 3.32 = 7.03784884 y = 7.03784884 Simplifying y = 7.03784884Subproblem 2
y + -3.32 = -3.71784884 Simplifying y + -3.32 = -3.71784884 Reorder the terms: -3.32 + y = -3.71784884 Solving -3.32 + y = -3.71784884 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.32' to each side of the equation. -3.32 + 3.32 + y = -3.71784884 + 3.32 Combine like terms: -3.32 + 3.32 = 0.00 0.00 + y = -3.71784884 + 3.32 y = -3.71784884 + 3.32 Combine like terms: -3.71784884 + 3.32 = -0.39784884 y = -0.39784884 Simplifying y = -0.39784884Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.03784884, -0.39784884}Solution
y = {0, 7.03784884, -0.39784884}
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