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Simplifying 2z2 + -12z + -36 = 0 Reorder the terms: -36 + -12z + 2z2 = 0 Solving -36 + -12z + 2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -6z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -6z + z2)' equal to zero and attempt to solve: Simplifying -18 + -6z + z2 = 0 Solving -18 + -6z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6z + 18 + z2 = 0 + 18 Reorder the terms: -18 + 18 + -6z + z2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6z + z2 = 0 + 18 -6z + z2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6z + z2 = 18 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 = 18 + 9 Reorder the terms: 9 + -6z + z2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6z + z2 = 27 Factor a perfect square on the left side: (z + -3)(z + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (z + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
z + -3 = 5.196152423 Simplifying z + -3 = 5.196152423 Reorder the terms: -3 + z = 5.196152423 Solving -3 + z = 5.196152423 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 = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + z = 5.196152423 + 3 z = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 z = 8.196152423 Simplifying z = 8.196152423Subproblem 2
z + -3 = -5.196152423 Simplifying z + -3 = -5.196152423 Reorder the terms: -3 + z = -5.196152423 Solving -3 + z = -5.196152423 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 = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + z = -5.196152423 + 3 z = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 z = -2.196152423 Simplifying z = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. z = {8.196152423, -2.196152423}Solution
z = {8.196152423, -2.196152423}
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