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Simplifying z2 + 18z + -5 = 0 Reorder the terms: -5 + 18z + z2 = 0 Solving -5 + 18z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 18z + 5 + z2 = 0 + 5 Reorder the terms: -5 + 5 + 18z + z2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 18z + z2 = 0 + 5 18z + z2 = 0 + 5 Combine like terms: 0 + 5 = 5 18z + z2 = 5 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 = 5 + 81 Reorder the terms: 81 + 18z + z2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + 18z + z2 = 86 Factor a perfect square on the left side: (z + 9)(z + 9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (z + 9) equal to 9.273618495 and -9.273618495.Subproblem 1
z + 9 = 9.273618495 Simplifying z + 9 = 9.273618495 Reorder the terms: 9 + z = 9.273618495 Solving 9 + z = 9.273618495 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 = 9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + z = 9.273618495 + -9 z = 9.273618495 + -9 Combine like terms: 9.273618495 + -9 = 0.273618495 z = 0.273618495 Simplifying z = 0.273618495Subproblem 2
z + 9 = -9.273618495 Simplifying z + 9 = -9.273618495 Reorder the terms: 9 + z = -9.273618495 Solving 9 + z = -9.273618495 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 = -9.273618495 + -9 Combine like terms: 9 + -9 = 0 0 + z = -9.273618495 + -9 z = -9.273618495 + -9 Combine like terms: -9.273618495 + -9 = -18.273618495 z = -18.273618495 Simplifying z = -18.273618495Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.273618495, -18.273618495}
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