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Simplifying 2 + 8z + z2 = 0 Solving 2 + 8z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 8z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + 8z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 8z + z2 = 0 + -2 8z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 8z + z2 = -2 The z term is 8z. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8z + 16 + z2 = -2 + 16 Reorder the terms: 16 + 8z + z2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + 8z + z2 = 14 Factor a perfect square on the left side: (z + 4)(z + 4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (z + 4) equal to 3.741657387 and -3.741657387.Subproblem 1
z + 4 = 3.741657387 Simplifying z + 4 = 3.741657387 Reorder the terms: 4 + z = 3.741657387 Solving 4 + z = 3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + z = 3.741657387 + -4 z = 3.741657387 + -4 Combine like terms: 3.741657387 + -4 = -0.258342613 z = -0.258342613 Simplifying z = -0.258342613Subproblem 2
z + 4 = -3.741657387 Simplifying z + 4 = -3.741657387 Reorder the terms: 4 + z = -3.741657387 Solving 4 + z = -3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + z = -3.741657387 + -4 z = -3.741657387 + -4 Combine like terms: -3.741657387 + -4 = -7.741657387 z = -7.741657387 Simplifying z = -7.741657387Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.258342613, -7.741657387}
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