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Simplifying z2 + -14z = -44 Reorder the terms: -14z + z2 = -44 Solving -14z + z2 = -44 Solving for variable 'z'. Reorder the terms: 44 + -14z + z2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + -14z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + -14z + -44 + z2 = 0 + -44 Reorder the terms: 44 + -44 + -14z + z2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -14z + z2 = 0 + -44 -14z + z2 = 0 + -44 Combine like terms: 0 + -44 = -44 -14z + z2 = -44 The z term is -14z. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14z + 49 + z2 = -44 + 49 Reorder the terms: 49 + -14z + z2 = -44 + 49 Combine like terms: -44 + 49 = 5 49 + -14z + z2 = 5 Factor a perfect square on the left side: (z + -7)(z + -7) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (z + -7) equal to 2.236067978 and -2.236067978.Subproblem 1
z + -7 = 2.236067978 Simplifying z + -7 = 2.236067978 Reorder the terms: -7 + z = 2.236067978 Solving -7 + z = 2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + z = 2.236067978 + 7 z = 2.236067978 + 7 Combine like terms: 2.236067978 + 7 = 9.236067978 z = 9.236067978 Simplifying z = 9.236067978Subproblem 2
z + -7 = -2.236067978 Simplifying z + -7 = -2.236067978 Reorder the terms: -7 + z = -2.236067978 Solving -7 + z = -2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + z = -2.236067978 + 7 z = -2.236067978 + 7 Combine like terms: -2.236067978 + 7 = 4.763932022 z = 4.763932022 Simplifying z = 4.763932022Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.236067978, 4.763932022}
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