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Simplifying z2 + 8z = 18 Reorder the terms: 8z + z2 = 18 Solving 8z + z2 = 18 Solving for variable 'z'. Reorder the terms: -18 + 8z + z2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 8z + 18 + z2 = 0 + 18 Reorder the terms: -18 + 18 + 8z + z2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8z + z2 = 0 + 18 8z + z2 = 0 + 18 Combine like terms: 0 + 18 = 18 8z + z2 = 18 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 = 18 + 16 Reorder the terms: 16 + 8z + z2 = 18 + 16 Combine like terms: 18 + 16 = 34 16 + 8z + z2 = 34 Factor a perfect square on the left side: (z + 4)(z + 4) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (z + 4) equal to 5.830951895 and -5.830951895.Subproblem 1
z + 4 = 5.830951895 Simplifying z + 4 = 5.830951895 Reorder the terms: 4 + z = 5.830951895 Solving 4 + z = 5.830951895 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 = 5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + z = 5.830951895 + -4 z = 5.830951895 + -4 Combine like terms: 5.830951895 + -4 = 1.830951895 z = 1.830951895 Simplifying z = 1.830951895Subproblem 2
z + 4 = -5.830951895 Simplifying z + 4 = -5.830951895 Reorder the terms: 4 + z = -5.830951895 Solving 4 + z = -5.830951895 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 = -5.830951895 + -4 Combine like terms: 4 + -4 = 0 0 + z = -5.830951895 + -4 z = -5.830951895 + -4 Combine like terms: -5.830951895 + -4 = -9.830951895 z = -9.830951895 Simplifying z = -9.830951895Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.830951895, -9.830951895}
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