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Simplifying z2 + -9z + 12 = 0 Reorder the terms: 12 + -9z + z2 = 0 Solving 12 + -9z + 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 + -9z + -12 + z2 = 0 + -12 Reorder the terms: 12 + -12 + -9z + z2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -9z + z2 = 0 + -12 -9z + z2 = 0 + -12 Combine like terms: 0 + -12 = -12 -9z + z2 = -12 The z term is -9z. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9z + 20.25 + z2 = -12 + 20.25 Reorder the terms: 20.25 + -9z + z2 = -12 + 20.25 Combine like terms: -12 + 20.25 = 8.25 20.25 + -9z + z2 = 8.25 Factor a perfect square on the left side: (z + -4.5)(z + -4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (z + -4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
z + -4.5 = 2.872281323 Simplifying z + -4.5 = 2.872281323 Reorder the terms: -4.5 + z = 2.872281323 Solving -4.5 + z = 2.872281323 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + z = 2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + z = 2.872281323 + 4.5 z = 2.872281323 + 4.5 Combine like terms: 2.872281323 + 4.5 = 7.372281323 z = 7.372281323 Simplifying z = 7.372281323Subproblem 2
z + -4.5 = -2.872281323 Simplifying z + -4.5 = -2.872281323 Reorder the terms: -4.5 + z = -2.872281323 Solving -4.5 + z = -2.872281323 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + z = -2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + z = -2.872281323 + 4.5 z = -2.872281323 + 4.5 Combine like terms: -2.872281323 + 4.5 = 1.627718677 z = 1.627718677 Simplifying z = 1.627718677Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.372281323, 1.627718677}
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