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Simplifying z2 + -4z + -24 = 0 Reorder the terms: -24 + -4z + z2 = 0 Solving -24 + -4z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -4z + 24 + z2 = 0 + 24 Reorder the terms: -24 + 24 + -4z + z2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4z + z2 = 0 + 24 -4z + z2 = 0 + 24 Combine like terms: 0 + 24 = 24 -4z + z2 = 24 The z term is -4z. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4z + 4 + z2 = 24 + 4 Reorder the terms: 4 + -4z + z2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + -4z + z2 = 28 Factor a perfect square on the left side: (z + -2)(z + -2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (z + -2) equal to 5.291502622 and -5.291502622.Subproblem 1
z + -2 = 5.291502622 Simplifying z + -2 = 5.291502622 Reorder the terms: -2 + z = 5.291502622 Solving -2 + z = 5.291502622 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + z = 5.291502622 + 2 z = 5.291502622 + 2 Combine like terms: 5.291502622 + 2 = 7.291502622 z = 7.291502622 Simplifying z = 7.291502622Subproblem 2
z + -2 = -5.291502622 Simplifying z + -2 = -5.291502622 Reorder the terms: -2 + z = -5.291502622 Solving -2 + z = -5.291502622 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + z = -5.291502622 + 2 z = -5.291502622 + 2 Combine like terms: -5.291502622 + 2 = -3.291502622 z = -3.291502622 Simplifying z = -3.291502622Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.291502622, -3.291502622}
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