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Simplifying -1y2 + 8y + 4 = 5 Reorder the terms: 4 + 8y + -1y2 = 5 Solving 4 + 8y + -1y2 = 5 Solving for variable 'y'. Reorder the terms: 4 + -5 + 8y + -1y2 = 5 + -5 Combine like terms: 4 + -5 = -1 -1 + 8y + -1y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -1 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -8y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -8y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8y + y2 = 0 + -1 -8y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8y + y2 = -1 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = -1 + 16 Reorder the terms: 16 + -8y + y2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8y + y2 = 15 Factor a perfect square on the left side: (y + -4)(y + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (y + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
y + -4 = 3.872983346 Simplifying y + -4 = 3.872983346 Reorder the terms: -4 + y = 3.872983346 Solving -4 + y = 3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + y = 3.872983346 + 4 y = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 y = 7.872983346 Simplifying y = 7.872983346Subproblem 2
y + -4 = -3.872983346 Simplifying y + -4 = -3.872983346 Reorder the terms: -4 + y = -3.872983346 Solving -4 + y = -3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + y = -3.872983346 + 4 y = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 y = 0.127016654 Simplifying y = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.872983346, 0.127016654}
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