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Simplifying 2z2 + 4z = 29 Reorder the terms: 4z + 2z2 = 29 Solving 4z + 2z2 = 29 Solving for variable 'z'. Reorder the terms: -29 + 4z + 2z2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 4z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + 2z + z2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + 2z + 14.5 + z2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + 2z + z2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + 2z + z2 = 0 + 14.5 2z + z2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 2z + z2 = 14.5 The z term is 2z. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2z + 1 + z2 = 14.5 + 1 Reorder the terms: 1 + 2z + z2 = 14.5 + 1 Combine like terms: 14.5 + 1 = 15.5 1 + 2z + z2 = 15.5 Factor a perfect square on the left side: (z + 1)(z + 1) = 15.5 Calculate the square root of the right side: 3.937003937 Break this problem into two subproblems by setting (z + 1) equal to 3.937003937 and -3.937003937.Subproblem 1
z + 1 = 3.937003937 Simplifying z + 1 = 3.937003937 Reorder the terms: 1 + z = 3.937003937 Solving 1 + z = 3.937003937 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 3.937003937 + -1 Combine like terms: 1 + -1 = 0 0 + z = 3.937003937 + -1 z = 3.937003937 + -1 Combine like terms: 3.937003937 + -1 = 2.937003937 z = 2.937003937 Simplifying z = 2.937003937Subproblem 2
z + 1 = -3.937003937 Simplifying z + 1 = -3.937003937 Reorder the terms: 1 + z = -3.937003937 Solving 1 + z = -3.937003937 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = -3.937003937 + -1 Combine like terms: 1 + -1 = 0 0 + z = -3.937003937 + -1 z = -3.937003937 + -1 Combine like terms: -3.937003937 + -1 = -4.937003937 z = -4.937003937 Simplifying z = -4.937003937Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.937003937, -4.937003937}
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