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Simplifying 3 + 8z + z2 = 0 Solving 3 + 8z + 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 + 8z + -3 + z2 = 0 + -3 Reorder the terms: 3 + -3 + 8z + z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8z + z2 = 0 + -3 8z + z2 = 0 + -3 Combine like terms: 0 + -3 = -3 8z + z2 = -3 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 = -3 + 16 Reorder the terms: 16 + 8z + z2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + 8z + z2 = 13 Factor a perfect square on the left side: (z + 4)(z + 4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (z + 4) equal to 3.605551275 and -3.605551275.Subproblem 1
z + 4 = 3.605551275 Simplifying z + 4 = 3.605551275 Reorder the terms: 4 + z = 3.605551275 Solving 4 + z = 3.605551275 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 = 3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + z = 3.605551275 + -4 z = 3.605551275 + -4 Combine like terms: 3.605551275 + -4 = -0.394448725 z = -0.394448725 Simplifying z = -0.394448725Subproblem 2
z + 4 = -3.605551275 Simplifying z + 4 = -3.605551275 Reorder the terms: 4 + z = -3.605551275 Solving 4 + z = -3.605551275 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 = -3.605551275 + -4 Combine like terms: 4 + -4 = 0 0 + z = -3.605551275 + -4 z = -3.605551275 + -4 Combine like terms: -3.605551275 + -4 = -7.605551275 z = -7.605551275 Simplifying z = -7.605551275Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.394448725, -7.605551275}
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