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Simplifying y2 + -14y + 44 = 0 Reorder the terms: 44 + -14y + y2 = 0 Solving 44 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + -14y + -44 + y2 = 0 + -44 Reorder the terms: 44 + -44 + -14y + y2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -14y + y2 = 0 + -44 -14y + y2 = 0 + -44 Combine like terms: 0 + -44 = -44 -14y + y2 = -44 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -44 + 49 Reorder the terms: 49 + -14y + y2 = -44 + 49 Combine like terms: -44 + 49 = 5 49 + -14y + y2 = 5 Factor a perfect square on the left side: (y + -7)(y + -7) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + -7) equal to 2.236067978 and -2.236067978.Subproblem 1
y + -7 = 2.236067978 Simplifying y + -7 = 2.236067978 Reorder the terms: -7 + y = 2.236067978 Solving -7 + y = 2.236067978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + y = 2.236067978 + 7 y = 2.236067978 + 7 Combine like terms: 2.236067978 + 7 = 9.236067978 y = 9.236067978 Simplifying y = 9.236067978Subproblem 2
y + -7 = -2.236067978 Simplifying y + -7 = -2.236067978 Reorder the terms: -7 + y = -2.236067978 Solving -7 + y = -2.236067978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + y = -2.236067978 + 7 y = -2.236067978 + 7 Combine like terms: -2.236067978 + 7 = 4.763932022 y = 4.763932022 Simplifying y = 4.763932022Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.236067978, 4.763932022}
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