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Simplifying 12Z + 12 + -1Z2 + -1 = 0 Reorder the terms: 12 + -1 + 12Z + -1Z2 = 0 Combine like terms: 12 + -1 = 11 11 + 12Z + -1Z2 = 0 Solving 11 + 12Z + -1Z2 = 0 Solving for variable 'Z'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -12Z + Z2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -12Z + 11 + Z2 = 0 + 11 Reorder the terms: -11 + 11 + -12Z + Z2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -12Z + Z2 = 0 + 11 -12Z + Z2 = 0 + 11 Combine like terms: 0 + 11 = 11 -12Z + Z2 = 11 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 = 11 + 36 Reorder the terms: 36 + -12Z + Z2 = 11 + 36 Combine like terms: 11 + 36 = 47 36 + -12Z + Z2 = 47 Factor a perfect square on the left side: (Z + -6)(Z + -6) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (Z + -6) equal to 6.8556546 and -6.8556546.Subproblem 1
Z + -6 = 6.8556546 Simplifying Z + -6 = 6.8556546 Reorder the terms: -6 + Z = 6.8556546 Solving -6 + Z = 6.8556546 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 = 6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + Z = 6.8556546 + 6 Z = 6.8556546 + 6 Combine like terms: 6.8556546 + 6 = 12.8556546 Z = 12.8556546 Simplifying Z = 12.8556546Subproblem 2
Z + -6 = -6.8556546 Simplifying Z + -6 = -6.8556546 Reorder the terms: -6 + Z = -6.8556546 Solving -6 + Z = -6.8556546 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 = -6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + Z = -6.8556546 + 6 Z = -6.8556546 + 6 Combine like terms: -6.8556546 + 6 = -0.8556546 Z = -0.8556546 Simplifying Z = -0.8556546Solution
The solution to the problem is based on the solutions from the subproblems. Z = {12.8556546, -0.8556546}
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