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Simplifying z2 + 14z + 8 = 0 Reorder the terms: 8 + 14z + z2 = 0 Solving 8 + 14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 14z + -8 + z2 = 0 + -8 Reorder the terms: 8 + -8 + 14z + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 14z + z2 = 0 + -8 14z + z2 = 0 + -8 Combine like terms: 0 + -8 = -8 14z + z2 = -8 The z term is 14z. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14z + 49 + z2 = -8 + 49 Reorder the terms: 49 + 14z + z2 = -8 + 49 Combine like terms: -8 + 49 = 41 49 + 14z + z2 = 41 Factor a perfect square on the left side: (z + 7)(z + 7) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (z + 7) equal to 6.403124237 and -6.403124237.Subproblem 1
z + 7 = 6.403124237 Simplifying z + 7 = 6.403124237 Reorder the terms: 7 + z = 6.403124237 Solving 7 + z = 6.403124237 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 6.403124237 + -7 Combine like terms: 7 + -7 = 0 0 + z = 6.403124237 + -7 z = 6.403124237 + -7 Combine like terms: 6.403124237 + -7 = -0.596875763 z = -0.596875763 Simplifying z = -0.596875763Subproblem 2
z + 7 = -6.403124237 Simplifying z + 7 = -6.403124237 Reorder the terms: 7 + z = -6.403124237 Solving 7 + z = -6.403124237 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = -6.403124237 + -7 Combine like terms: 7 + -7 = 0 0 + z = -6.403124237 + -7 z = -6.403124237 + -7 Combine like terms: -6.403124237 + -7 = -13.403124237 z = -13.403124237 Simplifying z = -13.403124237Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.596875763, -13.403124237}
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