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Simplifying z2 + 18z + 63 = 0 Reorder the terms: 63 + 18z + z2 = 0 Solving 63 + 18z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 18z + -63 + z2 = 0 + -63 Reorder the terms: 63 + -63 + 18z + z2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 18z + z2 = 0 + -63 18z + z2 = 0 + -63 Combine like terms: 0 + -63 = -63 18z + z2 = -63 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 = -63 + 81 Reorder the terms: 81 + 18z + z2 = -63 + 81 Combine like terms: -63 + 81 = 18 81 + 18z + z2 = 18 Factor a perfect square on the left side: (z + 9)(z + 9) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (z + 9) equal to 4.242640687 and -4.242640687.Subproblem 1
z + 9 = 4.242640687 Simplifying z + 9 = 4.242640687 Reorder the terms: 9 + z = 4.242640687 Solving 9 + z = 4.242640687 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 = 4.242640687 + -9 Combine like terms: 9 + -9 = 0 0 + z = 4.242640687 + -9 z = 4.242640687 + -9 Combine like terms: 4.242640687 + -9 = -4.757359313 z = -4.757359313 Simplifying z = -4.757359313Subproblem 2
z + 9 = -4.242640687 Simplifying z + 9 = -4.242640687 Reorder the terms: 9 + z = -4.242640687 Solving 9 + z = -4.242640687 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 = -4.242640687 + -9 Combine like terms: 9 + -9 = 0 0 + z = -4.242640687 + -9 z = -4.242640687 + -9 Combine like terms: -4.242640687 + -9 = -13.242640687 z = -13.242640687 Simplifying z = -13.242640687Solution
The solution to the problem is based on the solutions from the subproblems. z = {-4.757359313, -13.242640687}
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