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Simplifying 5Z2 + -55Z + 37 = 0 Reorder the terms: 37 + -55Z + 5Z2 = 0 Solving 37 + -55Z + 5Z2 = 0 Solving for variable 'Z'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.4 + -11Z + Z2 = 0 Move the constant term to the right: Add '-7.4' to each side of the equation. 7.4 + -11Z + -7.4 + Z2 = 0 + -7.4 Reorder the terms: 7.4 + -7.4 + -11Z + Z2 = 0 + -7.4 Combine like terms: 7.4 + -7.4 = 0.0 0.0 + -11Z + Z2 = 0 + -7.4 -11Z + Z2 = 0 + -7.4 Combine like terms: 0 + -7.4 = -7.4 -11Z + Z2 = -7.4 The Z term is -11Z. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11Z + 30.25 + Z2 = -7.4 + 30.25 Reorder the terms: 30.25 + -11Z + Z2 = -7.4 + 30.25 Combine like terms: -7.4 + 30.25 = 22.85 30.25 + -11Z + Z2 = 22.85 Factor a perfect square on the left side: (Z + -5.5)(Z + -5.5) = 22.85 Calculate the square root of the right side: 4.780167361 Break this problem into two subproblems by setting (Z + -5.5) equal to 4.780167361 and -4.780167361.Subproblem 1
Z + -5.5 = 4.780167361 Simplifying Z + -5.5 = 4.780167361 Reorder the terms: -5.5 + Z = 4.780167361 Solving -5.5 + Z = 4.780167361 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + Z = 4.780167361 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + Z = 4.780167361 + 5.5 Z = 4.780167361 + 5.5 Combine like terms: 4.780167361 + 5.5 = 10.280167361 Z = 10.280167361 Simplifying Z = 10.280167361Subproblem 2
Z + -5.5 = -4.780167361 Simplifying Z + -5.5 = -4.780167361 Reorder the terms: -5.5 + Z = -4.780167361 Solving -5.5 + Z = -4.780167361 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + Z = -4.780167361 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + Z = -4.780167361 + 5.5 Z = -4.780167361 + 5.5 Combine like terms: -4.780167361 + 5.5 = 0.719832639 Z = 0.719832639 Simplifying Z = 0.719832639Solution
The solution to the problem is based on the solutions from the subproblems. Z = {10.280167361, 0.719832639}
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