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Simplifying z2 + 16z + 80 = 166 Reorder the terms: 80 + 16z + z2 = 166 Solving 80 + 16z + z2 = 166 Solving for variable 'z'. Reorder the terms: 80 + -166 + 16z + z2 = 166 + -166 Combine like terms: 80 + -166 = -86 -86 + 16z + z2 = 166 + -166 Combine like terms: 166 + -166 = 0 -86 + 16z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + 16z + 86 + z2 = 0 + 86 Reorder the terms: -86 + 86 + 16z + z2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 16z + z2 = 0 + 86 16z + z2 = 0 + 86 Combine like terms: 0 + 86 = 86 16z + z2 = 86 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 = 86 + 64 Reorder the terms: 64 + 16z + z2 = 86 + 64 Combine like terms: 86 + 64 = 150 64 + 16z + z2 = 150 Factor a perfect square on the left side: (z + 8)(z + 8) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (z + 8) equal to 12.247448714 and -12.247448714.Subproblem 1
z + 8 = 12.247448714 Simplifying z + 8 = 12.247448714 Reorder the terms: 8 + z = 12.247448714 Solving 8 + z = 12.247448714 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 = 12.247448714 + -8 Combine like terms: 8 + -8 = 0 0 + z = 12.247448714 + -8 z = 12.247448714 + -8 Combine like terms: 12.247448714 + -8 = 4.247448714 z = 4.247448714 Simplifying z = 4.247448714Subproblem 2
z + 8 = -12.247448714 Simplifying z + 8 = -12.247448714 Reorder the terms: 8 + z = -12.247448714 Solving 8 + z = -12.247448714 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 = -12.247448714 + -8 Combine like terms: 8 + -8 = 0 0 + z = -12.247448714 + -8 z = -12.247448714 + -8 Combine like terms: -12.247448714 + -8 = -20.247448714 z = -20.247448714 Simplifying z = -20.247448714Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.247448714, -20.247448714}
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