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Simplifying 12z + z2 = 34 Solving 12z + z2 = 34 Solving for variable 'z'. Reorder the terms: -34 + 12z + z2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 12z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 12z + 34 + z2 = 0 + 34 Reorder the terms: -34 + 34 + 12z + z2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 12z + z2 = 0 + 34 12z + z2 = 0 + 34 Combine like terms: 0 + 34 = 34 12z + z2 = 34 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 = 34 + 36 Reorder the terms: 36 + 12z + z2 = 34 + 36 Combine like terms: 34 + 36 = 70 36 + 12z + z2 = 70 Factor a perfect square on the left side: (z + 6)(z + 6) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (z + 6) equal to 8.366600265 and -8.366600265.Subproblem 1
z + 6 = 8.366600265 Simplifying z + 6 = 8.366600265 Reorder the terms: 6 + z = 8.366600265 Solving 6 + z = 8.366600265 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 = 8.366600265 + -6 Combine like terms: 6 + -6 = 0 0 + z = 8.366600265 + -6 z = 8.366600265 + -6 Combine like terms: 8.366600265 + -6 = 2.366600265 z = 2.366600265 Simplifying z = 2.366600265Subproblem 2
z + 6 = -8.366600265 Simplifying z + 6 = -8.366600265 Reorder the terms: 6 + z = -8.366600265 Solving 6 + z = -8.366600265 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 = -8.366600265 + -6 Combine like terms: 6 + -6 = 0 0 + z = -8.366600265 + -6 z = -8.366600265 + -6 Combine like terms: -8.366600265 + -6 = -14.366600265 z = -14.366600265 Simplifying z = -14.366600265Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.366600265, -14.366600265}
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