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Simplifying z2 + 12z + -36 = 0 Reorder the terms: -36 + 12z + z2 = 0 Solving -36 + 12z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 12z + 36 + z2 = 0 + 36 Reorder the terms: -36 + 36 + 12z + z2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12z + z2 = 0 + 36 12z + z2 = 0 + 36 Combine like terms: 0 + 36 = 36 12z + z2 = 36 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 = 36 + 36 Reorder the terms: 36 + 12z + z2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12z + z2 = 72 Factor a perfect square on the left side: (z + 6)(z + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (z + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
z + 6 = 8.485281374 Simplifying z + 6 = 8.485281374 Reorder the terms: 6 + z = 8.485281374 Solving 6 + z = 8.485281374 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 = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + z = 8.485281374 + -6 z = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 z = 2.485281374 Simplifying z = 2.485281374Subproblem 2
z + 6 = -8.485281374 Simplifying z + 6 = -8.485281374 Reorder the terms: 6 + z = -8.485281374 Solving 6 + z = -8.485281374 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 = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + z = -8.485281374 + -6 z = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 z = -14.485281374 Simplifying z = -14.485281374Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.485281374, -14.485281374}
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