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Simplifying z2 + -20z = -17 Reorder the terms: -20z + z2 = -17 Solving -20z + z2 = -17 Solving for variable 'z'. Reorder the terms: 17 + -20z + z2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + -20z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -20z + -17 + z2 = 0 + -17 Reorder the terms: 17 + -17 + -20z + z2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -20z + z2 = 0 + -17 -20z + z2 = 0 + -17 Combine like terms: 0 + -17 = -17 -20z + z2 = -17 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 = -17 + 100 Reorder the terms: 100 + -20z + z2 = -17 + 100 Combine like terms: -17 + 100 = 83 100 + -20z + z2 = 83 Factor a perfect square on the left side: (z + -10)(z + -10) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (z + -10) equal to 9.110433579 and -9.110433579.Subproblem 1
z + -10 = 9.110433579 Simplifying z + -10 = 9.110433579 Reorder the terms: -10 + z = 9.110433579 Solving -10 + z = 9.110433579 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 = 9.110433579 + 10 Combine like terms: -10 + 10 = 0 0 + z = 9.110433579 + 10 z = 9.110433579 + 10 Combine like terms: 9.110433579 + 10 = 19.110433579 z = 19.110433579 Simplifying z = 19.110433579Subproblem 2
z + -10 = -9.110433579 Simplifying z + -10 = -9.110433579 Reorder the terms: -10 + z = -9.110433579 Solving -10 + z = -9.110433579 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 = -9.110433579 + 10 Combine like terms: -10 + 10 = 0 0 + z = -9.110433579 + 10 z = -9.110433579 + 10 Combine like terms: -9.110433579 + 10 = 0.889566421 z = 0.889566421 Simplifying z = 0.889566421Solution
The solution to the problem is based on the solutions from the subproblems. z = {19.110433579, 0.889566421}
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