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Simplifying 13y5 + 7y4 + -8y3 = 0 Reorder the terms: -8y3 + 7y4 + 13y5 = 0 Solving -8y3 + 7y4 + 13y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(-8 + 7y + 13y2) = 0Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-8 + 7y + 13y2)' equal to zero and attempt to solve: Simplifying -8 + 7y + 13y2 = 0 Solving -8 + 7y + 13y2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.6153846154 + 0.5384615385y + y2 = 0 Move the constant term to the right: Add '0.6153846154' to each side of the equation. -0.6153846154 + 0.5384615385y + 0.6153846154 + y2 = 0 + 0.6153846154 Reorder the terms: -0.6153846154 + 0.6153846154 + 0.5384615385y + y2 = 0 + 0.6153846154 Combine like terms: -0.6153846154 + 0.6153846154 = 0.0000000000 0.0000000000 + 0.5384615385y + y2 = 0 + 0.6153846154 0.5384615385y + y2 = 0 + 0.6153846154 Combine like terms: 0 + 0.6153846154 = 0.6153846154 0.5384615385y + y2 = 0.6153846154 The y term is 0.5384615385y. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385y + 0.07248520714 + y2 = 0.6153846154 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385y + y2 = 0.6153846154 + 0.07248520714 Combine like terms: 0.6153846154 + 0.07248520714 = 0.68786982254 0.07248520714 + 0.5384615385y + y2 = 0.68786982254 Factor a perfect square on the left side: (y + 0.2692307693)(y + 0.2692307693) = 0.68786982254 Calculate the square root of the right side: 0.829379179 Break this problem into two subproblems by setting (y + 0.2692307693) equal to 0.829379179 and -0.829379179.Subproblem 1
y + 0.2692307693 = 0.829379179 Simplifying y + 0.2692307693 = 0.829379179 Reorder the terms: 0.2692307693 + y = 0.829379179 Solving 0.2692307693 + y = 0.829379179 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + y = 0.829379179 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + y = 0.829379179 + -0.2692307693 y = 0.829379179 + -0.2692307693 Combine like terms: 0.829379179 + -0.2692307693 = 0.5601484097 y = 0.5601484097 Simplifying y = 0.5601484097Subproblem 2
y + 0.2692307693 = -0.829379179 Simplifying y + 0.2692307693 = -0.829379179 Reorder the terms: 0.2692307693 + y = -0.829379179 Solving 0.2692307693 + y = -0.829379179 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + y = -0.829379179 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + y = -0.829379179 + -0.2692307693 y = -0.829379179 + -0.2692307693 Combine like terms: -0.829379179 + -0.2692307693 = -1.0986099483 y = -1.0986099483 Simplifying y = -1.0986099483Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5601484097, -1.0986099483}Solution
y = {0.5601484097, -1.0986099483}
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