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Simplifying z2 + 12z + 22 = 0 Reorder the terms: 22 + 12z + z2 = 0 Solving 22 + 12z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 12z + -22 + z2 = 0 + -22 Reorder the terms: 22 + -22 + 12z + z2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 12z + z2 = 0 + -22 12z + z2 = 0 + -22 Combine like terms: 0 + -22 = -22 12z + z2 = -22 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 = -22 + 36 Reorder the terms: 36 + 12z + z2 = -22 + 36 Combine like terms: -22 + 36 = 14 36 + 12z + z2 = 14 Factor a perfect square on the left side: (z + 6)(z + 6) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (z + 6) equal to 3.741657387 and -3.741657387.Subproblem 1
z + 6 = 3.741657387 Simplifying z + 6 = 3.741657387 Reorder the terms: 6 + z = 3.741657387 Solving 6 + z = 3.741657387 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 = 3.741657387 + -6 Combine like terms: 6 + -6 = 0 0 + z = 3.741657387 + -6 z = 3.741657387 + -6 Combine like terms: 3.741657387 + -6 = -2.258342613 z = -2.258342613 Simplifying z = -2.258342613Subproblem 2
z + 6 = -3.741657387 Simplifying z + 6 = -3.741657387 Reorder the terms: 6 + z = -3.741657387 Solving 6 + z = -3.741657387 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 = -3.741657387 + -6 Combine like terms: 6 + -6 = 0 0 + z = -3.741657387 + -6 z = -3.741657387 + -6 Combine like terms: -3.741657387 + -6 = -9.741657387 z = -9.741657387 Simplifying z = -9.741657387Solution
The solution to the problem is based on the solutions from the subproblems. z = {-2.258342613, -9.741657387}
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