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Simplifying -1y2 + 8y = -7 Reorder the terms: 8y + -1y2 = -7 Solving 8y + -1y2 = -7 Solving for variable 'y'. Reorder the terms: 7 + 8y + -1y2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -8y + y2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -8y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -8y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8y + y2 = 0 + 7 -8y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8y + y2 = 7 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 = 7 + 16 Reorder the terms: 16 + -8y + y2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8y + y2 = 23 Factor a perfect square on the left side: (y + -4)(y + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (y + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
y + -4 = 4.795831523 Simplifying y + -4 = 4.795831523 Reorder the terms: -4 + y = 4.795831523 Solving -4 + y = 4.795831523 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 = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.795831523 + 4 y = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 y = 8.795831523 Simplifying y = 8.795831523Subproblem 2
y + -4 = -4.795831523 Simplifying y + -4 = -4.795831523 Reorder the terms: -4 + y = -4.795831523 Solving -4 + y = -4.795831523 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 = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.795831523 + 4 y = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 y = -0.795831523 Simplifying y = -0.795831523Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.795831523, -0.795831523}
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