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Simplifying z2 + -20z = -9 Reorder the terms: -20z + z2 = -9 Solving -20z + z2 = -9 Solving for variable 'z'. Reorder the terms: 9 + -20z + z2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -20z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -20z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + -20z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -20z + z2 = 0 + -9 -20z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 -20z + z2 = -9 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 = -9 + 100 Reorder the terms: 100 + -20z + z2 = -9 + 100 Combine like terms: -9 + 100 = 91 100 + -20z + z2 = 91 Factor a perfect square on the left side: (z + -10)(z + -10) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (z + -10) equal to 9.539392014 and -9.539392014.Subproblem 1
z + -10 = 9.539392014 Simplifying z + -10 = 9.539392014 Reorder the terms: -10 + z = 9.539392014 Solving -10 + z = 9.539392014 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 = 9.539392014 + 10 Combine like terms: -10 + 10 = 0 0 + z = 9.539392014 + 10 z = 9.539392014 + 10 Combine like terms: 9.539392014 + 10 = 19.539392014 z = 19.539392014 Simplifying z = 19.539392014Subproblem 2
z + -10 = -9.539392014 Simplifying z + -10 = -9.539392014 Reorder the terms: -10 + z = -9.539392014 Solving -10 + z = -9.539392014 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 = -9.539392014 + 10 Combine like terms: -10 + 10 = 0 0 + z = -9.539392014 + 10 z = -9.539392014 + 10 Combine like terms: -9.539392014 + 10 = 0.460607986 z = 0.460607986 Simplifying z = 0.460607986Solution
The solution to the problem is based on the solutions from the subproblems. z = {19.539392014, 0.460607986}
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