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Simplifying z2 + 12z = 20 Reorder the terms: 12z + z2 = 20 Solving 12z + z2 = 20 Solving for variable 'z'. Reorder the terms: -20 + 12z + z2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 12z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 12z + 20 + z2 = 0 + 20 Reorder the terms: -20 + 20 + 12z + z2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 12z + z2 = 0 + 20 12z + z2 = 0 + 20 Combine like terms: 0 + 20 = 20 12z + z2 = 20 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 = 20 + 36 Reorder the terms: 36 + 12z + z2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + 12z + z2 = 56 Factor a perfect square on the left side: (z + 6)(z + 6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (z + 6) equal to 7.483314774 and -7.483314774.Subproblem 1
z + 6 = 7.483314774 Simplifying z + 6 = 7.483314774 Reorder the terms: 6 + z = 7.483314774 Solving 6 + z = 7.483314774 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 = 7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + z = 7.483314774 + -6 z = 7.483314774 + -6 Combine like terms: 7.483314774 + -6 = 1.483314774 z = 1.483314774 Simplifying z = 1.483314774Subproblem 2
z + 6 = -7.483314774 Simplifying z + 6 = -7.483314774 Reorder the terms: 6 + z = -7.483314774 Solving 6 + z = -7.483314774 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 = -7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + z = -7.483314774 + -6 z = -7.483314774 + -6 Combine like terms: -7.483314774 + -6 = -13.483314774 z = -13.483314774 Simplifying z = -13.483314774Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.483314774, -13.483314774}
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