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Simplifying z2 = 8 + -6z Solving z2 = 8 + -6z Solving for variable 'z'. Reorder the terms: -8 + 6z + z2 = 8 + -6z + -8 + 6z Reorder the terms: -8 + 6z + z2 = 8 + -8 + -6z + 6z Combine like terms: 8 + -8 = 0 -8 + 6z + z2 = 0 + -6z + 6z -8 + 6z + z2 = -6z + 6z Combine like terms: -6z + 6z = 0 -8 + 6z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 6z + 8 + z2 = 0 + 8 Reorder the terms: -8 + 8 + 6z + z2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6z + z2 = 0 + 8 6z + z2 = 0 + 8 Combine like terms: 0 + 8 = 8 6z + z2 = 8 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 = 8 + 9 Reorder the terms: 9 + 6z + z2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6z + z2 = 17 Factor a perfect square on the left side: (z + 3)(z + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (z + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
z + 3 = 4.123105626 Simplifying z + 3 = 4.123105626 Reorder the terms: 3 + z = 4.123105626 Solving 3 + z = 4.123105626 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 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + z = 4.123105626 + -3 z = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 z = 1.123105626 Simplifying z = 1.123105626Subproblem 2
z + 3 = -4.123105626 Simplifying z + 3 = -4.123105626 Reorder the terms: 3 + z = -4.123105626 Solving 3 + z = -4.123105626 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 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + z = -4.123105626 + -3 z = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 z = -7.123105626 Simplifying z = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.123105626, -7.123105626}
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