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Simplifying -1z2 = -12z + 6 Reorder the terms: -1z2 = 6 + -12z Solving -1z2 = 6 + -12z Solving for variable 'z'. Reorder the terms: -6 + 12z + -1z2 = 6 + -12z + -6 + 12z Reorder the terms: -6 + 12z + -1z2 = 6 + -6 + -12z + 12z Combine like terms: 6 + -6 = 0 -6 + 12z + -1z2 = 0 + -12z + 12z -6 + 12z + -1z2 = -12z + 12z Combine like terms: -12z + 12z = 0 -6 + 12z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -12z + z2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -12z + -6 + z2 = 0 + -6 Reorder the terms: 6 + -6 + -12z + z2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -12z + z2 = 0 + -6 -12z + z2 = 0 + -6 Combine like terms: 0 + -6 = -6 -12z + z2 = -6 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 = -6 + 36 Reorder the terms: 36 + -12z + z2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + -12z + z2 = 30 Factor a perfect square on the left side: (z + -6)(z + -6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (z + -6) equal to 5.477225575 and -5.477225575.Subproblem 1
z + -6 = 5.477225575 Simplifying z + -6 = 5.477225575 Reorder the terms: -6 + z = 5.477225575 Solving -6 + z = 5.477225575 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 = 5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + z = 5.477225575 + 6 z = 5.477225575 + 6 Combine like terms: 5.477225575 + 6 = 11.477225575 z = 11.477225575 Simplifying z = 11.477225575Subproblem 2
z + -6 = -5.477225575 Simplifying z + -6 = -5.477225575 Reorder the terms: -6 + z = -5.477225575 Solving -6 + z = -5.477225575 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 = -5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + z = -5.477225575 + 6 z = -5.477225575 + 6 Combine like terms: -5.477225575 + 6 = 0.522774425 z = 0.522774425 Simplifying z = 0.522774425Solution
The solution to the problem is based on the solutions from the subproblems. z = {11.477225575, 0.522774425}
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