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Simplifying z2 + -6z + -12 = 0 Reorder the terms: -12 + -6z + z2 = 0 Solving -12 + -6z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -6z + 12 + z2 = 0 + 12 Reorder the terms: -12 + 12 + -6z + z2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6z + z2 = 0 + 12 -6z + z2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6z + z2 = 12 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 = 12 + 9 Reorder the terms: 9 + -6z + z2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + -6z + z2 = 21 Factor a perfect square on the left side: (z + -3)(z + -3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (z + -3) equal to 4.582575695 and -4.582575695.Subproblem 1
z + -3 = 4.582575695 Simplifying z + -3 = 4.582575695 Reorder the terms: -3 + z = 4.582575695 Solving -3 + z = 4.582575695 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 = 4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + z = 4.582575695 + 3 z = 4.582575695 + 3 Combine like terms: 4.582575695 + 3 = 7.582575695 z = 7.582575695 Simplifying z = 7.582575695Subproblem 2
z + -3 = -4.582575695 Simplifying z + -3 = -4.582575695 Reorder the terms: -3 + z = -4.582575695 Solving -3 + z = -4.582575695 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 = -4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + z = -4.582575695 + 3 z = -4.582575695 + 3 Combine like terms: -4.582575695 + 3 = -1.582575695 z = -1.582575695 Simplifying z = -1.582575695Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.582575695, -1.582575695}
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