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Simplifying z2 + 22z + 19 = 0 Reorder the terms: 19 + 22z + z2 = 0 Solving 19 + 22z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 22z + -19 + z2 = 0 + -19 Reorder the terms: 19 + -19 + 22z + z2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 22z + z2 = 0 + -19 22z + z2 = 0 + -19 Combine like terms: 0 + -19 = -19 22z + z2 = -19 The z term is 22z. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22z + 121 + z2 = -19 + 121 Reorder the terms: 121 + 22z + z2 = -19 + 121 Combine like terms: -19 + 121 = 102 121 + 22z + z2 = 102 Factor a perfect square on the left side: (z + 11)(z + 11) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (z + 11) equal to 10.099504938 and -10.099504938.Subproblem 1
z + 11 = 10.099504938 Simplifying z + 11 = 10.099504938 Reorder the terms: 11 + z = 10.099504938 Solving 11 + z = 10.099504938 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + z = 10.099504938 + -11 Combine like terms: 11 + -11 = 0 0 + z = 10.099504938 + -11 z = 10.099504938 + -11 Combine like terms: 10.099504938 + -11 = -0.900495062 z = -0.900495062 Simplifying z = -0.900495062Subproblem 2
z + 11 = -10.099504938 Simplifying z + 11 = -10.099504938 Reorder the terms: 11 + z = -10.099504938 Solving 11 + z = -10.099504938 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + z = -10.099504938 + -11 Combine like terms: 11 + -11 = 0 0 + z = -10.099504938 + -11 z = -10.099504938 + -11 Combine like terms: -10.099504938 + -11 = -21.099504938 z = -21.099504938 Simplifying z = -21.099504938Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.900495062, -21.099504938}
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