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Simplifying z2 + 16z + 52 = 0 Reorder the terms: 52 + 16z + z2 = 0 Solving 52 + 16z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 16z + -52 + z2 = 0 + -52 Reorder the terms: 52 + -52 + 16z + z2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 16z + z2 = 0 + -52 16z + z2 = 0 + -52 Combine like terms: 0 + -52 = -52 16z + z2 = -52 The z term is 16z. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16z + 64 + z2 = -52 + 64 Reorder the terms: 64 + 16z + z2 = -52 + 64 Combine like terms: -52 + 64 = 12 64 + 16z + z2 = 12 Factor a perfect square on the left side: (z + 8)(z + 8) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (z + 8) equal to 3.464101615 and -3.464101615.Subproblem 1
z + 8 = 3.464101615 Simplifying z + 8 = 3.464101615 Reorder the terms: 8 + z = 3.464101615 Solving 8 + z = 3.464101615 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 3.464101615 + -8 Combine like terms: 8 + -8 = 0 0 + z = 3.464101615 + -8 z = 3.464101615 + -8 Combine like terms: 3.464101615 + -8 = -4.535898385 z = -4.535898385 Simplifying z = -4.535898385Subproblem 2
z + 8 = -3.464101615 Simplifying z + 8 = -3.464101615 Reorder the terms: 8 + z = -3.464101615 Solving 8 + z = -3.464101615 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = -3.464101615 + -8 Combine like terms: 8 + -8 = 0 0 + z = -3.464101615 + -8 z = -3.464101615 + -8 Combine like terms: -3.464101615 + -8 = -11.464101615 z = -11.464101615 Simplifying z = -11.464101615Solution
The solution to the problem is based on the solutions from the subproblems. z = {-4.535898385, -11.464101615}
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