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Simplifying 35y2 + -120y + -100 = 0 Reorder the terms: -100 + -120y + 35y2 = 0 Solving -100 + -120y + 35y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + -24y + 7y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + -24y + 7y2)' equal to zero and attempt to solve: Simplifying -20 + -24y + 7y2 = 0 Solving -20 + -24y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + -3.428571429y + y2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -3.428571429y + 2.857142857 + y2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -3.428571429y + y2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -3.428571429y + y2 = 0 + 2.857142857 -3.428571429y + y2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -3.428571429y + y2 = 2.857142857 The y term is -3.428571429y. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429y + 2.938775513 + y2 = 2.857142857 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429y + y2 = 2.857142857 + 2.938775513 Combine like terms: 2.857142857 + 2.938775513 = 5.79591837 2.938775513 + -3.428571429y + y2 = 5.79591837 Factor a perfect square on the left side: (y + -1.714285715)(y + -1.714285715) = 5.79591837 Calculate the square root of the right side: 2.407471364 Break this problem into two subproblems by setting (y + -1.714285715) equal to 2.407471364 and -2.407471364.Subproblem 1
y + -1.714285715 = 2.407471364 Simplifying y + -1.714285715 = 2.407471364 Reorder the terms: -1.714285715 + y = 2.407471364 Solving -1.714285715 + y = 2.407471364 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + y = 2.407471364 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + y = 2.407471364 + 1.714285715 y = 2.407471364 + 1.714285715 Combine like terms: 2.407471364 + 1.714285715 = 4.121757079 y = 4.121757079 Simplifying y = 4.121757079Subproblem 2
y + -1.714285715 = -2.407471364 Simplifying y + -1.714285715 = -2.407471364 Reorder the terms: -1.714285715 + y = -2.407471364 Solving -1.714285715 + y = -2.407471364 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + y = -2.407471364 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + y = -2.407471364 + 1.714285715 y = -2.407471364 + 1.714285715 Combine like terms: -2.407471364 + 1.714285715 = -0.693185649 y = -0.693185649 Simplifying y = -0.693185649Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.121757079, -0.693185649}Solution
y = {4.121757079, -0.693185649}
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