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Simplifying 0 = y2 + -4y + -92 Reorder the terms: 0 = -92 + -4y + y2 Solving 0 = -92 + -4y + y2 Solving for variable 'y'. Combine like terms: 0 + 92 = 92 92 + 4y + -1y2 = -92 + -4y + y2 + 92 + 4y + -1y2 Reorder the terms: 92 + 4y + -1y2 = -92 + 92 + -4y + 4y + y2 + -1y2 Combine like terms: -92 + 92 = 0 92 + 4y + -1y2 = 0 + -4y + 4y + y2 + -1y2 92 + 4y + -1y2 = -4y + 4y + y2 + -1y2 Combine like terms: -4y + 4y = 0 92 + 4y + -1y2 = 0 + y2 + -1y2 92 + 4y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 92 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -92 + -4y + y2 = 0 Move the constant term to the right: Add '92' to each side of the equation. -92 + -4y + 92 + y2 = 0 + 92 Reorder the terms: -92 + 92 + -4y + y2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + -4y + y2 = 0 + 92 -4y + y2 = 0 + 92 Combine like terms: 0 + 92 = 92 -4y + y2 = 92 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 92 + 4 Reorder the terms: 4 + -4y + y2 = 92 + 4 Combine like terms: 92 + 4 = 96 4 + -4y + y2 = 96 Factor a perfect square on the left side: (y + -2)(y + -2) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (y + -2) equal to 9.797958971 and -9.797958971.Subproblem 1
y + -2 = 9.797958971 Simplifying y + -2 = 9.797958971 Reorder the terms: -2 + y = 9.797958971 Solving -2 + y = 9.797958971 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 9.797958971 + 2 Combine like terms: -2 + 2 = 0 0 + y = 9.797958971 + 2 y = 9.797958971 + 2 Combine like terms: 9.797958971 + 2 = 11.797958971 y = 11.797958971 Simplifying y = 11.797958971Subproblem 2
y + -2 = -9.797958971 Simplifying y + -2 = -9.797958971 Reorder the terms: -2 + y = -9.797958971 Solving -2 + y = -9.797958971 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -9.797958971 + 2 Combine like terms: -2 + 2 = 0 0 + y = -9.797958971 + 2 y = -9.797958971 + 2 Combine like terms: -9.797958971 + 2 = -7.797958971 y = -7.797958971 Simplifying y = -7.797958971Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.797958971, -7.797958971}
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