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Simplifying z2 + 14z + 10 = 0 Reorder the terms: 10 + 14z + z2 = 0 Solving 10 + 14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 14z + -10 + z2 = 0 + -10 Reorder the terms: 10 + -10 + 14z + z2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 14z + z2 = 0 + -10 14z + z2 = 0 + -10 Combine like terms: 0 + -10 = -10 14z + z2 = -10 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 = -10 + 49 Reorder the terms: 49 + 14z + z2 = -10 + 49 Combine like terms: -10 + 49 = 39 49 + 14z + z2 = 39 Factor a perfect square on the left side: (z + 7)(z + 7) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (z + 7) equal to 6.244997998 and -6.244997998.Subproblem 1
z + 7 = 6.244997998 Simplifying z + 7 = 6.244997998 Reorder the terms: 7 + z = 6.244997998 Solving 7 + z = 6.244997998 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 = 6.244997998 + -7 Combine like terms: 7 + -7 = 0 0 + z = 6.244997998 + -7 z = 6.244997998 + -7 Combine like terms: 6.244997998 + -7 = -0.755002002 z = -0.755002002 Simplifying z = -0.755002002Subproblem 2
z + 7 = -6.244997998 Simplifying z + 7 = -6.244997998 Reorder the terms: 7 + z = -6.244997998 Solving 7 + z = -6.244997998 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 = -6.244997998 + -7 Combine like terms: 7 + -7 = 0 0 + z = -6.244997998 + -7 z = -6.244997998 + -7 Combine like terms: -6.244997998 + -7 = -13.244997998 z = -13.244997998 Simplifying z = -13.244997998Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.755002002, -13.244997998}
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