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Simplifying z2 + 16z = -5 Reorder the terms: 16z + z2 = -5 Solving 16z + z2 = -5 Solving for variable 'z'. Reorder the terms: 5 + 16z + z2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 16z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 16z + -5 + z2 = 0 + -5 Reorder the terms: 5 + -5 + 16z + z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 16z + z2 = 0 + -5 16z + z2 = 0 + -5 Combine like terms: 0 + -5 = -5 16z + z2 = -5 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 = -5 + 64 Reorder the terms: 64 + 16z + z2 = -5 + 64 Combine like terms: -5 + 64 = 59 64 + 16z + z2 = 59 Factor a perfect square on the left side: (z + 8)(z + 8) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (z + 8) equal to 7.681145748 and -7.681145748.Subproblem 1
z + 8 = 7.681145748 Simplifying z + 8 = 7.681145748 Reorder the terms: 8 + z = 7.681145748 Solving 8 + z = 7.681145748 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 = 7.681145748 + -8 Combine like terms: 8 + -8 = 0 0 + z = 7.681145748 + -8 z = 7.681145748 + -8 Combine like terms: 7.681145748 + -8 = -0.318854252 z = -0.318854252 Simplifying z = -0.318854252Subproblem 2
z + 8 = -7.681145748 Simplifying z + 8 = -7.681145748 Reorder the terms: 8 + z = -7.681145748 Solving 8 + z = -7.681145748 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 = -7.681145748 + -8 Combine like terms: 8 + -8 = 0 0 + z = -7.681145748 + -8 z = -7.681145748 + -8 Combine like terms: -7.681145748 + -8 = -15.681145748 z = -15.681145748 Simplifying z = -15.681145748Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.318854252, -15.681145748}
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