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Simplifying 8y2 + -22y + -108 = 0 Reorder the terms: -108 + -22y + 8y2 = 0 Solving -108 + -22y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + -11y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + -11y + 4y2)' equal to zero and attempt to solve: Simplifying -54 + -11y + 4y2 = 0 Solving -54 + -11y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.5 + -2.75y + y2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -2.75y + 13.5 + y2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -2.75y + y2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -2.75y + y2 = 0 + 13.5 -2.75y + y2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -2.75y + y2 = 13.5 The y term is -2.75y. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75y + 1.890625 + y2 = 13.5 + 1.890625 Reorder the terms: 1.890625 + -2.75y + y2 = 13.5 + 1.890625 Combine like terms: 13.5 + 1.890625 = 15.390625 1.890625 + -2.75y + y2 = 15.390625 Factor a perfect square on the left side: (y + -1.375)(y + -1.375) = 15.390625 Calculate the square root of the right side: 3.923088707 Break this problem into two subproblems by setting (y + -1.375) equal to 3.923088707 and -3.923088707.Subproblem 1
y + -1.375 = 3.923088707 Simplifying y + -1.375 = 3.923088707 Reorder the terms: -1.375 + y = 3.923088707 Solving -1.375 + y = 3.923088707 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + y = 3.923088707 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + y = 3.923088707 + 1.375 y = 3.923088707 + 1.375 Combine like terms: 3.923088707 + 1.375 = 5.298088707 y = 5.298088707 Simplifying y = 5.298088707Subproblem 2
y + -1.375 = -3.923088707 Simplifying y + -1.375 = -3.923088707 Reorder the terms: -1.375 + y = -3.923088707 Solving -1.375 + y = -3.923088707 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + y = -3.923088707 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + y = -3.923088707 + 1.375 y = -3.923088707 + 1.375 Combine like terms: -3.923088707 + 1.375 = -2.548088707 y = -2.548088707 Simplifying y = -2.548088707Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.298088707, -2.548088707}Solution
y = {5.298088707, -2.548088707}
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