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Simplifying y3 + -5y2 + -35y = 3y2 Reorder the terms: -35y + -5y2 + y3 = 3y2 Solving -35y + -5y2 + y3 = 3y2 Solving for variable 'y'. Reorder the terms: -35y + -5y2 + -3y2 + y3 = 3y2 + -3y2 Combine like terms: -5y2 + -3y2 = -8y2 -35y + -8y2 + y3 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -35y + -8y2 + y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(-35 + -8y + y2) = 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 '(-35 + -8y + y2)' equal to zero and attempt to solve: Simplifying -35 + -8y + y2 = 0 Solving -35 + -8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -8y + 35 + y2 = 0 + 35 Reorder the terms: -35 + 35 + -8y + y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -8y + y2 = 0 + 35 -8y + y2 = 0 + 35 Combine like terms: 0 + 35 = 35 -8y + y2 = 35 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 35 + 16 Reorder the terms: 16 + -8y + y2 = 35 + 16 Combine like terms: 35 + 16 = 51 16 + -8y + y2 = 51 Factor a perfect square on the left side: (y + -4)(y + -4) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (y + -4) equal to 7.141428429 and -7.141428429.Subproblem 1
y + -4 = 7.141428429 Simplifying y + -4 = 7.141428429 Reorder the terms: -4 + y = 7.141428429 Solving -4 + y = 7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 7.141428429 + 4 Combine like terms: -4 + 4 = 0 0 + y = 7.141428429 + 4 y = 7.141428429 + 4 Combine like terms: 7.141428429 + 4 = 11.141428429 y = 11.141428429 Simplifying y = 11.141428429Subproblem 2
y + -4 = -7.141428429 Simplifying y + -4 = -7.141428429 Reorder the terms: -4 + y = -7.141428429 Solving -4 + y = -7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -7.141428429 + 4 Combine like terms: -4 + 4 = 0 0 + y = -7.141428429 + 4 y = -7.141428429 + 4 Combine like terms: -7.141428429 + 4 = -3.141428429 y = -3.141428429 Simplifying y = -3.141428429Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.141428429, -3.141428429}Solution
y = {0, 11.141428429, -3.141428429}
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