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Simplifying z2 + -18z = -15 Reorder the terms: -18z + z2 = -15 Solving -18z + z2 = -15 Solving for variable 'z'. Reorder the terms: 15 + -18z + z2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -18z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -18z + -15 + z2 = 0 + -15 Reorder the terms: 15 + -15 + -18z + z2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -18z + z2 = 0 + -15 -18z + z2 = 0 + -15 Combine like terms: 0 + -15 = -15 -18z + z2 = -15 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 = -15 + 81 Reorder the terms: 81 + -18z + z2 = -15 + 81 Combine like terms: -15 + 81 = 66 81 + -18z + z2 = 66 Factor a perfect square on the left side: (z + -9)(z + -9) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (z + -9) equal to 8.124038405 and -8.124038405.Subproblem 1
z + -9 = 8.124038405 Simplifying z + -9 = 8.124038405 Reorder the terms: -9 + z = 8.124038405 Solving -9 + z = 8.124038405 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 = 8.124038405 + 9 Combine like terms: -9 + 9 = 0 0 + z = 8.124038405 + 9 z = 8.124038405 + 9 Combine like terms: 8.124038405 + 9 = 17.124038405 z = 17.124038405 Simplifying z = 17.124038405Subproblem 2
z + -9 = -8.124038405 Simplifying z + -9 = -8.124038405 Reorder the terms: -9 + z = -8.124038405 Solving -9 + z = -8.124038405 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 = -8.124038405 + 9 Combine like terms: -9 + 9 = 0 0 + z = -8.124038405 + 9 z = -8.124038405 + 9 Combine like terms: -8.124038405 + 9 = 0.875961595 z = 0.875961595 Simplifying z = 0.875961595Solution
The solution to the problem is based on the solutions from the subproblems. z = {17.124038405, 0.875961595}
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