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Simplifying 3z2 + -36z + 13 = 0 Reorder the terms: 13 + -36z + 3z2 = 0 Solving 13 + -36z + 3z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + -12z + z2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -12z + -4.333333333 + z2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -12z + z2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -12z + z2 = 0 + -4.333333333 -12z + z2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -12z + z2 = -4.333333333 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 = -4.333333333 + 36 Reorder the terms: 36 + -12z + z2 = -4.333333333 + 36 Combine like terms: -4.333333333 + 36 = 31.666666667 36 + -12z + z2 = 31.666666667 Factor a perfect square on the left side: (z + -6)(z + -6) = 31.666666667 Calculate the square root of the right side: 5.627314339 Break this problem into two subproblems by setting (z + -6) equal to 5.627314339 and -5.627314339.Subproblem 1
z + -6 = 5.627314339 Simplifying z + -6 = 5.627314339 Reorder the terms: -6 + z = 5.627314339 Solving -6 + z = 5.627314339 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 = 5.627314339 + 6 Combine like terms: -6 + 6 = 0 0 + z = 5.627314339 + 6 z = 5.627314339 + 6 Combine like terms: 5.627314339 + 6 = 11.627314339 z = 11.627314339 Simplifying z = 11.627314339Subproblem 2
z + -6 = -5.627314339 Simplifying z + -6 = -5.627314339 Reorder the terms: -6 + z = -5.627314339 Solving -6 + z = -5.627314339 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 = -5.627314339 + 6 Combine like terms: -6 + 6 = 0 0 + z = -5.627314339 + 6 z = -5.627314339 + 6 Combine like terms: -5.627314339 + 6 = 0.372685661 z = 0.372685661 Simplifying z = 0.372685661Solution
The solution to the problem is based on the solutions from the subproblems. z = {11.627314339, 0.372685661}
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