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Simplifying 3 + 9z + z2 = 0 Solving 3 + 9z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 9z + -3 + z2 = 0 + -3 Reorder the terms: 3 + -3 + 9z + z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 9z + z2 = 0 + -3 9z + z2 = 0 + -3 Combine like terms: 0 + -3 = -3 9z + z2 = -3 The z term is 9z. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9z + 20.25 + z2 = -3 + 20.25 Reorder the terms: 20.25 + 9z + z2 = -3 + 20.25 Combine like terms: -3 + 20.25 = 17.25 20.25 + 9z + z2 = 17.25 Factor a perfect square on the left side: (z + 4.5)(z + 4.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (z + 4.5) equal to 4.153311931 and -4.153311931.Subproblem 1
z + 4.5 = 4.153311931 Simplifying z + 4.5 = 4.153311931 Reorder the terms: 4.5 + z = 4.153311931 Solving 4.5 + z = 4.153311931 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = 4.153311931 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = 4.153311931 + -4.5 z = 4.153311931 + -4.5 Combine like terms: 4.153311931 + -4.5 = -0.346688069 z = -0.346688069 Simplifying z = -0.346688069Subproblem 2
z + 4.5 = -4.153311931 Simplifying z + 4.5 = -4.153311931 Reorder the terms: 4.5 + z = -4.153311931 Solving 4.5 + z = -4.153311931 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = -4.153311931 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = -4.153311931 + -4.5 z = -4.153311931 + -4.5 Combine like terms: -4.153311931 + -4.5 = -8.653311931 z = -8.653311931 Simplifying z = -8.653311931Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.346688069, -8.653311931}
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