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Simplifying -1y2 + 2y + 23 = 0 Reorder the terms: 23 + 2y + -1y2 = 0 Solving 23 + 2y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + -2y + y2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + -2y + 23 + y2 = 0 + 23 Reorder the terms: -23 + 23 + -2y + y2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -2y + y2 = 0 + 23 -2y + y2 = 0 + 23 Combine like terms: 0 + 23 = 23 -2y + y2 = 23 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 23 + 1 Reorder the terms: 1 + -2y + y2 = 23 + 1 Combine like terms: 23 + 1 = 24 1 + -2y + y2 = 24 Factor a perfect square on the left side: (y + -1)(y + -1) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (y + -1) equal to 4.898979486 and -4.898979486.Subproblem 1
y + -1 = 4.898979486 Simplifying y + -1 = 4.898979486 Reorder the terms: -1 + y = 4.898979486 Solving -1 + y = 4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 4.898979486 + 1 Combine like terms: -1 + 1 = 0 0 + y = 4.898979486 + 1 y = 4.898979486 + 1 Combine like terms: 4.898979486 + 1 = 5.898979486 y = 5.898979486 Simplifying y = 5.898979486Subproblem 2
y + -1 = -4.898979486 Simplifying y + -1 = -4.898979486 Reorder the terms: -1 + y = -4.898979486 Solving -1 + y = -4.898979486 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -4.898979486 + 1 Combine like terms: -1 + 1 = 0 0 + y = -4.898979486 + 1 y = -4.898979486 + 1 Combine like terms: -4.898979486 + 1 = -3.898979486 y = -3.898979486 Simplifying y = -3.898979486Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.898979486, -3.898979486}
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