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Simplifying 8y2 + -96y + 20 = 0 Reorder the terms: 20 + -96y + 8y2 = 0 Solving 20 + -96y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -24y + 2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -24y + 2y2)' equal to zero and attempt to solve: Simplifying 5 + -24y + 2y2 = 0 Solving 5 + -24y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -12y + y2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -12y + -2.5 + y2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -12y + y2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -12y + y2 = 0 + -2.5 -12y + y2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -12y + y2 = -2.5 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -2.5 + 36 Reorder the terms: 36 + -12y + y2 = -2.5 + 36 Combine like terms: -2.5 + 36 = 33.5 36 + -12y + y2 = 33.5 Factor a perfect square on the left side: (y + -6)(y + -6) = 33.5 Calculate the square root of the right side: 5.787918451 Break this problem into two subproblems by setting (y + -6) equal to 5.787918451 and -5.787918451.Subproblem 1
y + -6 = 5.787918451 Simplifying y + -6 = 5.787918451 Reorder the terms: -6 + y = 5.787918451 Solving -6 + y = 5.787918451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 5.787918451 + 6 Combine like terms: -6 + 6 = 0 0 + y = 5.787918451 + 6 y = 5.787918451 + 6 Combine like terms: 5.787918451 + 6 = 11.787918451 y = 11.787918451 Simplifying y = 11.787918451Subproblem 2
y + -6 = -5.787918451 Simplifying y + -6 = -5.787918451 Reorder the terms: -6 + y = -5.787918451 Solving -6 + y = -5.787918451 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -5.787918451 + 6 Combine like terms: -6 + 6 = 0 0 + y = -5.787918451 + 6 y = -5.787918451 + 6 Combine like terms: -5.787918451 + 6 = 0.212081549 y = 0.212081549 Simplifying y = 0.212081549Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.787918451, 0.212081549}Solution
y = {11.787918451, 0.212081549}
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