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Simplifying z2 + 20z = 41 Reorder the terms: 20z + z2 = 41 Solving 20z + z2 = 41 Solving for variable 'z'. Reorder the terms: -41 + 20z + z2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 20z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 20z + 41 + z2 = 0 + 41 Reorder the terms: -41 + 41 + 20z + z2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 20z + z2 = 0 + 41 20z + z2 = 0 + 41 Combine like terms: 0 + 41 = 41 20z + z2 = 41 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 = 41 + 100 Reorder the terms: 100 + 20z + z2 = 41 + 100 Combine like terms: 41 + 100 = 141 100 + 20z + z2 = 141 Factor a perfect square on the left side: (z + 10)(z + 10) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (z + 10) equal to 11.874342087 and -11.874342087.Subproblem 1
z + 10 = 11.874342087 Simplifying z + 10 = 11.874342087 Reorder the terms: 10 + z = 11.874342087 Solving 10 + z = 11.874342087 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 = 11.874342087 + -10 Combine like terms: 10 + -10 = 0 0 + z = 11.874342087 + -10 z = 11.874342087 + -10 Combine like terms: 11.874342087 + -10 = 1.874342087 z = 1.874342087 Simplifying z = 1.874342087Subproblem 2
z + 10 = -11.874342087 Simplifying z + 10 = -11.874342087 Reorder the terms: 10 + z = -11.874342087 Solving 10 + z = -11.874342087 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 = -11.874342087 + -10 Combine like terms: 10 + -10 = 0 0 + z = -11.874342087 + -10 z = -11.874342087 + -10 Combine like terms: -11.874342087 + -10 = -21.874342087 z = -21.874342087 Simplifying z = -21.874342087Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.874342087, -21.874342087}
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