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Simplifying 7Z2 + 36Z = 5 Reorder the terms: 36Z + 7Z2 = 5 Solving 36Z + 7Z2 = 5 Solving for variable 'Z'. Reorder the terms: -5 + 36Z + 7Z2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 36Z + 7Z2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 5.142857143Z + Z2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 5.142857143Z + 0.7142857143 + Z2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 5.142857143Z + Z2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 5.142857143Z + Z2 = 0 + 0.7142857143 5.142857143Z + Z2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 5.142857143Z + Z2 = 0.7142857143 The Z term is 5.142857143Z. Take half its coefficient (2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. 5.142857143Z + 6.612244901 + Z2 = 0.7142857143 + 6.612244901 Reorder the terms: 6.612244901 + 5.142857143Z + Z2 = 0.7142857143 + 6.612244901 Combine like terms: 0.7142857143 + 6.612244901 = 7.3265306153 6.612244901 + 5.142857143Z + Z2 = 7.3265306153 Factor a perfect square on the left side: (Z + 2.571428572)(Z + 2.571428572) = 7.3265306153 Calculate the square root of the right side: 2.706756475 Break this problem into two subproblems by setting (Z + 2.571428572) equal to 2.706756475 and -2.706756475.Subproblem 1
Z + 2.571428572 = 2.706756475 Simplifying Z + 2.571428572 = 2.706756475 Reorder the terms: 2.571428572 + Z = 2.706756475 Solving 2.571428572 + Z = 2.706756475 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + Z = 2.706756475 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + Z = 2.706756475 + -2.571428572 Z = 2.706756475 + -2.571428572 Combine like terms: 2.706756475 + -2.571428572 = 0.135327903 Z = 0.135327903 Simplifying Z = 0.135327903Subproblem 2
Z + 2.571428572 = -2.706756475 Simplifying Z + 2.571428572 = -2.706756475 Reorder the terms: 2.571428572 + Z = -2.706756475 Solving 2.571428572 + Z = -2.706756475 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + Z = -2.706756475 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + Z = -2.706756475 + -2.571428572 Z = -2.706756475 + -2.571428572 Combine like terms: -2.706756475 + -2.571428572 = -5.278185047 Z = -5.278185047 Simplifying Z = -5.278185047Solution
The solution to the problem is based on the solutions from the subproblems. Z = {0.135327903, -5.278185047}
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