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Simplifying 1 + -0.6Z + 0.08Z2 = 0 Solving 1 + -0.6Z + 0.08Z2 = 0 Solving for variable 'Z'. Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. 12.5 + -7.5Z + Z2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -7.5Z + -12.5 + Z2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -7.5Z + Z2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -7.5Z + Z2 = 0 + -12.5 -7.5Z + Z2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -7.5Z + Z2 = -12.5 The Z term is -7.5Z. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5Z + 14.0625 + Z2 = -12.5 + 14.0625 Reorder the terms: 14.0625 + -7.5Z + Z2 = -12.5 + 14.0625 Combine like terms: -12.5 + 14.0625 = 1.5625 14.0625 + -7.5Z + Z2 = 1.5625 Factor a perfect square on the left side: (Z + -3.75)(Z + -3.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (Z + -3.75) equal to 1.25 and -1.25.Subproblem 1
Z + -3.75 = 1.25 Simplifying Z + -3.75 = 1.25 Reorder the terms: -3.75 + Z = 1.25 Solving -3.75 + Z = 1.25 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + Z = 1.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + Z = 1.25 + 3.75 Z = 1.25 + 3.75 Combine like terms: 1.25 + 3.75 = 5 Z = 5 Simplifying Z = 5Subproblem 2
Z + -3.75 = -1.25 Simplifying Z + -3.75 = -1.25 Reorder the terms: -3.75 + Z = -1.25 Solving -3.75 + Z = -1.25 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + Z = -1.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + Z = -1.25 + 3.75 Z = -1.25 + 3.75 Combine like terms: -1.25 + 3.75 = 2.5 Z = 2.5 Simplifying Z = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. Z = {5, 2.5}
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