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Simplifying z2 + 16z + -29 = 0 Reorder the terms: -29 + 16z + z2 = 0 Solving -29 + 16z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 16z + 29 + z2 = 0 + 29 Reorder the terms: -29 + 29 + 16z + z2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 16z + z2 = 0 + 29 16z + z2 = 0 + 29 Combine like terms: 0 + 29 = 29 16z + z2 = 29 The z term is 16z. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16z + 64 + z2 = 29 + 64 Reorder the terms: 64 + 16z + z2 = 29 + 64 Combine like terms: 29 + 64 = 93 64 + 16z + z2 = 93 Factor a perfect square on the left side: (z + 8)(z + 8) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (z + 8) equal to 9.643650761 and -9.643650761.Subproblem 1
z + 8 = 9.643650761 Simplifying z + 8 = 9.643650761 Reorder the terms: 8 + z = 9.643650761 Solving 8 + z = 9.643650761 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 9.643650761 + -8 Combine like terms: 8 + -8 = 0 0 + z = 9.643650761 + -8 z = 9.643650761 + -8 Combine like terms: 9.643650761 + -8 = 1.643650761 z = 1.643650761 Simplifying z = 1.643650761Subproblem 2
z + 8 = -9.643650761 Simplifying z + 8 = -9.643650761 Reorder the terms: 8 + z = -9.643650761 Solving 8 + z = -9.643650761 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = -9.643650761 + -8 Combine like terms: 8 + -8 = 0 0 + z = -9.643650761 + -8 z = -9.643650761 + -8 Combine like terms: -9.643650761 + -8 = -17.643650761 z = -17.643650761 Simplifying z = -17.643650761Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.643650761, -17.643650761}
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