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Simplifying 3y3 + -7y = 3y2 + 25y Reorder the terms: -7y + 3y3 = 3y2 + 25y Reorder the terms: -7y + 3y3 = 25y + 3y2 Solving -7y + 3y3 = 25y + 3y2 Solving for variable 'y'. Reorder the terms: -7y + -25y + -3y2 + 3y3 = 25y + 3y2 + -25y + -3y2 Combine like terms: -7y + -25y = -32y -32y + -3y2 + 3y3 = 25y + 3y2 + -25y + -3y2 Reorder the terms: -32y + -3y2 + 3y3 = 25y + -25y + 3y2 + -3y2 Combine like terms: 25y + -25y = 0 -32y + -3y2 + 3y3 = 0 + 3y2 + -3y2 -32y + -3y2 + 3y3 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -32y + -3y2 + 3y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-32 + -3y + 3y2) = 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 '(-32 + -3y + 3y2)' equal to zero and attempt to solve: Simplifying -32 + -3y + 3y2 = 0 Solving -32 + -3y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + -1y + y2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -1y + 10.66666667 + y2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -1y + y2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -1y + y2 = 0 + 10.66666667 -1y + y2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -1y + y2 = 10.66666667 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 10.66666667 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 10.66666667 + 0.25 Combine like terms: 10.66666667 + 0.25 = 10.91666667 0.25 + -1y + y2 = 10.91666667 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 10.91666667 Calculate the square root of the right side: 3.304037934 Break this problem into two subproblems by setting (y + -0.5) equal to 3.304037934 and -3.304037934.Subproblem 1
y + -0.5 = 3.304037934 Simplifying y + -0.5 = 3.304037934 Reorder the terms: -0.5 + y = 3.304037934 Solving -0.5 + y = 3.304037934 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 3.304037934 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 3.304037934 + 0.5 y = 3.304037934 + 0.5 Combine like terms: 3.304037934 + 0.5 = 3.804037934 y = 3.804037934 Simplifying y = 3.804037934Subproblem 2
y + -0.5 = -3.304037934 Simplifying y + -0.5 = -3.304037934 Reorder the terms: -0.5 + y = -3.304037934 Solving -0.5 + y = -3.304037934 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -3.304037934 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -3.304037934 + 0.5 y = -3.304037934 + 0.5 Combine like terms: -3.304037934 + 0.5 = -2.804037934 y = -2.804037934 Simplifying y = -2.804037934Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.804037934, -2.804037934}Solution
y = {0, 3.804037934, -2.804037934}
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