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Simplifying y2 + -8y = -11 Reorder the terms: -8y + y2 = -11 Solving -8y + y2 = -11 Solving for variable 'y'. Reorder the terms: 11 + -8y + y2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8y + -11 + y2 = 0 + -11 Reorder the terms: 11 + -11 + -8y + y2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8y + y2 = 0 + -11 -8y + y2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8y + y2 = -11 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 = -11 + 16 Reorder the terms: 16 + -8y + y2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + -8y + y2 = 5 Factor a perfect square on the left side: (y + -4)(y + -4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + -4) equal to 2.236067978 and -2.236067978.Subproblem 1
y + -4 = 2.236067978 Simplifying y + -4 = 2.236067978 Reorder the terms: -4 + y = 2.236067978 Solving -4 + y = 2.236067978 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 = 2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + y = 2.236067978 + 4 y = 2.236067978 + 4 Combine like terms: 2.236067978 + 4 = 6.236067978 y = 6.236067978 Simplifying y = 6.236067978Subproblem 2
y + -4 = -2.236067978 Simplifying y + -4 = -2.236067978 Reorder the terms: -4 + y = -2.236067978 Solving -4 + y = -2.236067978 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 = -2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + y = -2.236067978 + 4 y = -2.236067978 + 4 Combine like terms: -2.236067978 + 4 = 1.763932022 y = 1.763932022 Simplifying y = 1.763932022Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.236067978, 1.763932022}
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