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Simplifying z2 + 20z + 2 = 0 Reorder the terms: 2 + 20z + z2 = 0 Solving 2 + 20z + 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 + 20z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + 20z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 20z + z2 = 0 + -2 20z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 20z + z2 = -2 The z term is 20z. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20z + 100 + z2 = -2 + 100 Reorder the terms: 100 + 20z + z2 = -2 + 100 Combine like terms: -2 + 100 = 98 100 + 20z + z2 = 98 Factor a perfect square on the left side: (z + 10)(z + 10) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (z + 10) equal to 9.899494937 and -9.899494937.Subproblem 1
z + 10 = 9.899494937 Simplifying z + 10 = 9.899494937 Reorder the terms: 10 + z = 9.899494937 Solving 10 + z = 9.899494937 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + z = 9.899494937 + -10 Combine like terms: 10 + -10 = 0 0 + z = 9.899494937 + -10 z = 9.899494937 + -10 Combine like terms: 9.899494937 + -10 = -0.100505063 z = -0.100505063 Simplifying z = -0.100505063Subproblem 2
z + 10 = -9.899494937 Simplifying z + 10 = -9.899494937 Reorder the terms: 10 + z = -9.899494937 Solving 10 + z = -9.899494937 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + z = -9.899494937 + -10 Combine like terms: 10 + -10 = 0 0 + z = -9.899494937 + -10 z = -9.899494937 + -10 Combine like terms: -9.899494937 + -10 = -19.899494937 z = -19.899494937 Simplifying z = -19.899494937Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.100505063, -19.899494937}
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