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Simplifying z2 + 12z + 18 = 0 Reorder the terms: 18 + 12z + z2 = 0 Solving 18 + 12z + 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 + 12z + -18 + z2 = 0 + -18 Reorder the terms: 18 + -18 + 12z + z2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 12z + z2 = 0 + -18 12z + z2 = 0 + -18 Combine like terms: 0 + -18 = -18 12z + z2 = -18 The z term is 12z. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12z + 36 + z2 = -18 + 36 Reorder the terms: 36 + 12z + z2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + 12z + z2 = 18 Factor a perfect square on the left side: (z + 6)(z + 6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (z + 6) equal to 4.242640687 and -4.242640687.Subproblem 1
z + 6 = 4.242640687 Simplifying z + 6 = 4.242640687 Reorder the terms: 6 + z = 4.242640687 Solving 6 + z = 4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + z = 4.242640687 + -6 z = 4.242640687 + -6 Combine like terms: 4.242640687 + -6 = -1.757359313 z = -1.757359313 Simplifying z = -1.757359313Subproblem 2
z + 6 = -4.242640687 Simplifying z + 6 = -4.242640687 Reorder the terms: 6 + z = -4.242640687 Solving 6 + z = -4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = -4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + z = -4.242640687 + -6 z = -4.242640687 + -6 Combine like terms: -4.242640687 + -6 = -10.242640687 z = -10.242640687 Simplifying z = -10.242640687Solution
The solution to the problem is based on the solutions from the subproblems. z = {-1.757359313, -10.242640687}
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