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Simplifying z2 + 8z + 9 = 0 Reorder the terms: 9 + 8z + z2 = 0 Solving 9 + 8z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + 8z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8z + z2 = 0 + -9 8z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 8z + z2 = -9 The z term is 8z. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8z + 16 + z2 = -9 + 16 Reorder the terms: 16 + 8z + z2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8z + z2 = 7 Factor a perfect square on the left side: (z + 4)(z + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (z + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
z + 4 = 2.645751311 Simplifying z + 4 = 2.645751311 Reorder the terms: 4 + z = 2.645751311 Solving 4 + z = 2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + z = 2.645751311 + -4 z = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 z = -1.354248689 Simplifying z = -1.354248689Subproblem 2
z + 4 = -2.645751311 Simplifying z + 4 = -2.645751311 Reorder the terms: 4 + z = -2.645751311 Solving 4 + z = -2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + z = -2.645751311 + -4 z = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 z = -6.645751311 Simplifying z = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. z = {-1.354248689, -6.645751311}
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