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Simplifying z2 + -10z + 18 = 0 Reorder the terms: 18 + -10z + z2 = 0 Solving 18 + -10z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10z + -18 + z2 = 0 + -18 Reorder the terms: 18 + -18 + -10z + z2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10z + z2 = 0 + -18 -10z + z2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10z + z2 = -18 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = -18 + 25 Reorder the terms: 25 + -10z + z2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10z + z2 = 7 Factor a perfect square on the left side: (z + -5)(z + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (z + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
z + -5 = 2.645751311 Simplifying z + -5 = 2.645751311 Reorder the terms: -5 + z = 2.645751311 Solving -5 + z = 2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + z = 2.645751311 + 5 z = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 z = 7.645751311 Simplifying z = 7.645751311Subproblem 2
z + -5 = -2.645751311 Simplifying z + -5 = -2.645751311 Reorder the terms: -5 + z = -2.645751311 Solving -5 + z = -2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + z = -2.645751311 + 5 z = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 z = 2.354248689 Simplifying z = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.645751311, 2.354248689}
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