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Simplifying z2 + 18z + 62 = 0 Reorder the terms: 62 + 18z + z2 = 0 Solving 62 + 18z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + 18z + -62 + z2 = 0 + -62 Reorder the terms: 62 + -62 + 18z + z2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + 18z + z2 = 0 + -62 18z + z2 = 0 + -62 Combine like terms: 0 + -62 = -62 18z + z2 = -62 The z term is 18z. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18z + 81 + z2 = -62 + 81 Reorder the terms: 81 + 18z + z2 = -62 + 81 Combine like terms: -62 + 81 = 19 81 + 18z + z2 = 19 Factor a perfect square on the left side: (z + 9)(z + 9) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (z + 9) equal to 4.358898944 and -4.358898944.Subproblem 1
z + 9 = 4.358898944 Simplifying z + 9 = 4.358898944 Reorder the terms: 9 + z = 4.358898944 Solving 9 + z = 4.358898944 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 4.358898944 + -9 Combine like terms: 9 + -9 = 0 0 + z = 4.358898944 + -9 z = 4.358898944 + -9 Combine like terms: 4.358898944 + -9 = -4.641101056 z = -4.641101056 Simplifying z = -4.641101056Subproblem 2
z + 9 = -4.358898944 Simplifying z + 9 = -4.358898944 Reorder the terms: 9 + z = -4.358898944 Solving 9 + z = -4.358898944 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = -4.358898944 + -9 Combine like terms: 9 + -9 = 0 0 + z = -4.358898944 + -9 z = -4.358898944 + -9 Combine like terms: -4.358898944 + -9 = -13.358898944 z = -13.358898944 Simplifying z = -13.358898944Solution
The solution to the problem is based on the solutions from the subproblems. z = {-4.641101056, -13.358898944}
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