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Simplifying 10y4 + -35y3 + -5y2 = 5y2 Reorder the terms: -5y2 + -35y3 + 10y4 = 5y2 Solving -5y2 + -35y3 + 10y4 = 5y2 Solving for variable 'y'. Reorder the terms: -5y2 + -5y2 + -35y3 + 10y4 = 5y2 + -5y2 Combine like terms: -5y2 + -5y2 = -10y2 -10y2 + -35y3 + 10y4 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 -10y2 + -35y3 + 10y4 = 0 Factor out the Greatest Common Factor (GCF), '5y2'. 5y2(-2 + -7y + 2y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-2 + -7y + 2y2)' equal to zero and attempt to solve: Simplifying -2 + -7y + 2y2 = 0 Solving -2 + -7y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -3.5y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.5y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -3.5y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.5y + y2 = 0 + 1 -3.5y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.5y + y2 = 1 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 1 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 1 + 3.0625 Combine like terms: 1 + 3.0625 = 4.0625 3.0625 + -3.5y + y2 = 4.0625 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (y + -1.75) equal to 2.015564437 and -2.015564437.Subproblem 1
y + -1.75 = 2.015564437 Simplifying y + -1.75 = 2.015564437 Reorder the terms: -1.75 + y = 2.015564437 Solving -1.75 + y = 2.015564437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 2.015564437 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 2.015564437 + 1.75 y = 2.015564437 + 1.75 Combine like terms: 2.015564437 + 1.75 = 3.765564437 y = 3.765564437 Simplifying y = 3.765564437Subproblem 2
y + -1.75 = -2.015564437 Simplifying y + -1.75 = -2.015564437 Reorder the terms: -1.75 + y = -2.015564437 Solving -1.75 + y = -2.015564437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -2.015564437 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -2.015564437 + 1.75 y = -2.015564437 + 1.75 Combine like terms: -2.015564437 + 1.75 = -0.265564437 y = -0.265564437 Simplifying y = -0.265564437Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.765564437, -0.265564437}Solution
y = {0, 3.765564437, -0.265564437}
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