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Simplifying z2 + -18z = -11 Reorder the terms: -18z + z2 = -11 Solving -18z + z2 = -11 Solving for variable 'z'. Reorder the terms: 11 + -18z + z2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -18z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -18z + -11 + z2 = 0 + -11 Reorder the terms: 11 + -11 + -18z + z2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -18z + z2 = 0 + -11 -18z + z2 = 0 + -11 Combine like terms: 0 + -11 = -11 -18z + z2 = -11 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 = -11 + 81 Reorder the terms: 81 + -18z + z2 = -11 + 81 Combine like terms: -11 + 81 = 70 81 + -18z + z2 = 70 Factor a perfect square on the left side: (z + -9)(z + -9) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (z + -9) equal to 8.366600265 and -8.366600265.Subproblem 1
z + -9 = 8.366600265 Simplifying z + -9 = 8.366600265 Reorder the terms: -9 + z = 8.366600265 Solving -9 + z = 8.366600265 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 = 8.366600265 + 9 Combine like terms: -9 + 9 = 0 0 + z = 8.366600265 + 9 z = 8.366600265 + 9 Combine like terms: 8.366600265 + 9 = 17.366600265 z = 17.366600265 Simplifying z = 17.366600265Subproblem 2
z + -9 = -8.366600265 Simplifying z + -9 = -8.366600265 Reorder the terms: -9 + z = -8.366600265 Solving -9 + z = -8.366600265 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 = -8.366600265 + 9 Combine like terms: -9 + 9 = 0 0 + z = -8.366600265 + 9 z = -8.366600265 + 9 Combine like terms: -8.366600265 + 9 = 0.633399735 z = 0.633399735 Simplifying z = 0.633399735Solution
The solution to the problem is based on the solutions from the subproblems. z = {17.366600265, 0.633399735}
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