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Simplifying z2 + 47z + 18 = 0 Reorder the terms: 18 + 47z + z2 = 0 Solving 18 + 47z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 47z + -18 + z2 = 0 + -18 Reorder the terms: 18 + -18 + 47z + z2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 47z + z2 = 0 + -18 47z + z2 = 0 + -18 Combine like terms: 0 + -18 = -18 47z + z2 = -18 The z term is 47z. Take half its coefficient (23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. 47z + 552.25 + z2 = -18 + 552.25 Reorder the terms: 552.25 + 47z + z2 = -18 + 552.25 Combine like terms: -18 + 552.25 = 534.25 552.25 + 47z + z2 = 534.25 Factor a perfect square on the left side: (z + 23.5)(z + 23.5) = 534.25 Calculate the square root of the right side: 23.113848663 Break this problem into two subproblems by setting (z + 23.5) equal to 23.113848663 and -23.113848663.Subproblem 1
z + 23.5 = 23.113848663 Simplifying z + 23.5 = 23.113848663 Reorder the terms: 23.5 + z = 23.113848663 Solving 23.5 + z = 23.113848663 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + z = 23.113848663 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + z = 23.113848663 + -23.5 z = 23.113848663 + -23.5 Combine like terms: 23.113848663 + -23.5 = -0.386151337 z = -0.386151337 Simplifying z = -0.386151337Subproblem 2
z + 23.5 = -23.113848663 Simplifying z + 23.5 = -23.113848663 Reorder the terms: 23.5 + z = -23.113848663 Solving 23.5 + z = -23.113848663 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + z = -23.113848663 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + z = -23.113848663 + -23.5 z = -23.113848663 + -23.5 Combine like terms: -23.113848663 + -23.5 = -46.613848663 z = -46.613848663 Simplifying z = -46.613848663Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.386151337, -46.613848663}
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