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Simplifying -3z2 + 36z = -33 Reorder the terms: 36z + -3z2 = -33 Solving 36z + -3z2 = -33 Solving for variable 'z'. Reorder the terms: 33 + 36z + -3z2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + 36z + -3z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + 12z + -1z2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + 12z + -1z2)' equal to zero and attempt to solve: Simplifying 11 + 12z + -1z2 = 0 Solving 11 + 12z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -12z + z2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -12z + 11 + z2 = 0 + 11 Reorder the terms: -11 + 11 + -12z + z2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -12z + z2 = 0 + 11 -12z + z2 = 0 + 11 Combine like terms: 0 + 11 = 11 -12z + z2 = 11 The z term is -12z. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12z + 36 + z2 = 11 + 36 Reorder the terms: 36 + -12z + z2 = 11 + 36 Combine like terms: 11 + 36 = 47 36 + -12z + z2 = 47 Factor a perfect square on the left side: (z + -6)(z + -6) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (z + -6) equal to 6.8556546 and -6.8556546.Subproblem 1
z + -6 = 6.8556546 Simplifying z + -6 = 6.8556546 Reorder the terms: -6 + z = 6.8556546 Solving -6 + z = 6.8556546 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + z = 6.8556546 + 6 z = 6.8556546 + 6 Combine like terms: 6.8556546 + 6 = 12.8556546 z = 12.8556546 Simplifying z = 12.8556546Subproblem 2
z + -6 = -6.8556546 Simplifying z + -6 = -6.8556546 Reorder the terms: -6 + z = -6.8556546 Solving -6 + z = -6.8556546 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = -6.8556546 + 6 Combine like terms: -6 + 6 = 0 0 + z = -6.8556546 + 6 z = -6.8556546 + 6 Combine like terms: -6.8556546 + 6 = -0.8556546 z = -0.8556546 Simplifying z = -0.8556546Solution
The solution to the problem is based on the solutions from the subproblems. z = {12.8556546, -0.8556546}Solution
z = {12.8556546, -0.8556546}
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