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Simplifying 4z2 + -29z + -4 = 0 Reorder the terms: -4 + -29z + 4z2 = 0 Solving -4 + -29z + 4z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -7.25z + z2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -7.25z + 1 + z2 = 0 + 1 Reorder the terms: -1 + 1 + -7.25z + z2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7.25z + z2 = 0 + 1 -7.25z + z2 = 0 + 1 Combine like terms: 0 + 1 = 1 -7.25z + z2 = 1 The z term is -7.25z. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25z + 13.140625 + z2 = 1 + 13.140625 Reorder the terms: 13.140625 + -7.25z + z2 = 1 + 13.140625 Combine like terms: 1 + 13.140625 = 14.140625 13.140625 + -7.25z + z2 = 14.140625 Factor a perfect square on the left side: (z + -3.625)(z + -3.625) = 14.140625 Calculate the square root of the right side: 3.760402239 Break this problem into two subproblems by setting (z + -3.625) equal to 3.760402239 and -3.760402239.Subproblem 1
z + -3.625 = 3.760402239 Simplifying z + -3.625 = 3.760402239 Reorder the terms: -3.625 + z = 3.760402239 Solving -3.625 + z = 3.760402239 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + z = 3.760402239 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + z = 3.760402239 + 3.625 z = 3.760402239 + 3.625 Combine like terms: 3.760402239 + 3.625 = 7.385402239 z = 7.385402239 Simplifying z = 7.385402239Subproblem 2
z + -3.625 = -3.760402239 Simplifying z + -3.625 = -3.760402239 Reorder the terms: -3.625 + z = -3.760402239 Solving -3.625 + z = -3.760402239 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + z = -3.760402239 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + z = -3.760402239 + 3.625 z = -3.760402239 + 3.625 Combine like terms: -3.760402239 + 3.625 = -0.135402239 z = -0.135402239 Simplifying z = -0.135402239Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.385402239, -0.135402239}
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