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Simplifying z2 + -18z + -81 = 0 Reorder the terms: -81 + -18z + z2 = 0 Solving -81 + -18z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -18z + 81 + z2 = 0 + 81 Reorder the terms: -81 + 81 + -18z + z2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -18z + z2 = 0 + 81 -18z + z2 = 0 + 81 Combine like terms: 0 + 81 = 81 -18z + z2 = 81 The z term is -18z. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18z + 81 + z2 = 81 + 81 Reorder the terms: 81 + -18z + z2 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + -18z + z2 = 162 Factor a perfect square on the left side: (z + -9)(z + -9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (z + -9) equal to 12.727922061 and -12.727922061.Subproblem 1
z + -9 = 12.727922061 Simplifying z + -9 = 12.727922061 Reorder the terms: -9 + z = 12.727922061 Solving -9 + z = 12.727922061 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + z = 12.727922061 + 9 z = 12.727922061 + 9 Combine like terms: 12.727922061 + 9 = 21.727922061 z = 21.727922061 Simplifying z = 21.727922061Subproblem 2
z + -9 = -12.727922061 Simplifying z + -9 = -12.727922061 Reorder the terms: -9 + z = -12.727922061 Solving -9 + z = -12.727922061 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = -12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + z = -12.727922061 + 9 z = -12.727922061 + 9 Combine like terms: -12.727922061 + 9 = -3.727922061 z = -3.727922061 Simplifying z = -3.727922061Solution
The solution to the problem is based on the solutions from the subproblems. z = {21.727922061, -3.727922061}
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