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Simplifying y = y2 + 3y + -4 Reorder the terms: y = -4 + 3y + y2 Solving y = -4 + 3y + y2 Solving for variable 'y'. Reorder the terms: 4 + y + -3y + -1y2 = -4 + 3y + y2 + 4 + -3y + -1y2 Combine like terms: y + -3y = -2y 4 + -2y + -1y2 = -4 + 3y + y2 + 4 + -3y + -1y2 Reorder the terms: 4 + -2y + -1y2 = -4 + 4 + 3y + -3y + y2 + -1y2 Combine like terms: -4 + 4 = 0 4 + -2y + -1y2 = 0 + 3y + -3y + y2 + -1y2 4 + -2y + -1y2 = 3y + -3y + y2 + -1y2 Combine like terms: 3y + -3y = 0 4 + -2y + -1y2 = 0 + y2 + -1y2 4 + -2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 4 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 2y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 2y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2y + y2 = 0 + 4 2y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 2y + y2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2y + y2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2y + y2 = 5 Factor a perfect square on the left side: (y + 1)(y + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + 1) equal to 2.236067978 and -2.236067978.Subproblem 1
y + 1 = 2.236067978 Simplifying y + 1 = 2.236067978 Reorder the terms: 1 + y = 2.236067978 Solving 1 + y = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + y = 2.236067978 + -1 y = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 y = 1.236067978 Simplifying y = 1.236067978Subproblem 2
y + 1 = -2.236067978 Simplifying y + 1 = -2.236067978 Reorder the terms: 1 + y = -2.236067978 Solving 1 + y = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + y = -2.236067978 + -1 y = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 y = -3.236067978 Simplifying y = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.236067978, -3.236067978}
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