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Simplifying z2 + 6z + -4 = 0 Reorder the terms: -4 + 6z + z2 = 0 Solving -4 + 6z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6z + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + 6z + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6z + z2 = 0 + 4 6z + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 6z + z2 = 4 The z term is 6z. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6z + 9 + z2 = 4 + 9 Reorder the terms: 9 + 6z + z2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6z + z2 = 13 Factor a perfect square on the left side: (z + 3)(z + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (z + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
z + 3 = 3.605551275 Simplifying z + 3 = 3.605551275 Reorder the terms: 3 + z = 3.605551275 Solving 3 + z = 3.605551275 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + z = 3.605551275 + -3 z = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 z = 0.605551275 Simplifying z = 0.605551275Subproblem 2
z + 3 = -3.605551275 Simplifying z + 3 = -3.605551275 Reorder the terms: 3 + z = -3.605551275 Solving 3 + z = -3.605551275 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + z = -3.605551275 + -3 z = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 z = -6.605551275 Simplifying z = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.605551275, -6.605551275}
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