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Simplifying z2 + 14z + 14 = 0 Reorder the terms: 14 + 14z + z2 = 0 Solving 14 + 14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 14z + -14 + z2 = 0 + -14 Reorder the terms: 14 + -14 + 14z + z2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 14z + z2 = 0 + -14 14z + z2 = 0 + -14 Combine like terms: 0 + -14 = -14 14z + z2 = -14 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 = -14 + 49 Reorder the terms: 49 + 14z + z2 = -14 + 49 Combine like terms: -14 + 49 = 35 49 + 14z + z2 = 35 Factor a perfect square on the left side: (z + 7)(z + 7) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (z + 7) equal to 5.916079783 and -5.916079783.Subproblem 1
z + 7 = 5.916079783 Simplifying z + 7 = 5.916079783 Reorder the terms: 7 + z = 5.916079783 Solving 7 + z = 5.916079783 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 = 5.916079783 + -7 Combine like terms: 7 + -7 = 0 0 + z = 5.916079783 + -7 z = 5.916079783 + -7 Combine like terms: 5.916079783 + -7 = -1.083920217 z = -1.083920217 Simplifying z = -1.083920217Subproblem 2
z + 7 = -5.916079783 Simplifying z + 7 = -5.916079783 Reorder the terms: 7 + z = -5.916079783 Solving 7 + z = -5.916079783 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 = -5.916079783 + -7 Combine like terms: 7 + -7 = 0 0 + z = -5.916079783 + -7 z = -5.916079783 + -7 Combine like terms: -5.916079783 + -7 = -12.916079783 z = -12.916079783 Simplifying z = -12.916079783Solution
The solution to the problem is based on the solutions from the subproblems. z = {-1.083920217, -12.916079783}
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