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Simplifying z2 + 22z + -21 = 0 Reorder the terms: -21 + 22z + z2 = 0 Solving -21 + 22z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 22z + 21 + z2 = 0 + 21 Reorder the terms: -21 + 21 + 22z + z2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 22z + z2 = 0 + 21 22z + z2 = 0 + 21 Combine like terms: 0 + 21 = 21 22z + z2 = 21 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 = 21 + 121 Reorder the terms: 121 + 22z + z2 = 21 + 121 Combine like terms: 21 + 121 = 142 121 + 22z + z2 = 142 Factor a perfect square on the left side: (z + 11)(z + 11) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (z + 11) equal to 11.916375288 and -11.916375288.Subproblem 1
z + 11 = 11.916375288 Simplifying z + 11 = 11.916375288 Reorder the terms: 11 + z = 11.916375288 Solving 11 + z = 11.916375288 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 = 11.916375288 + -11 Combine like terms: 11 + -11 = 0 0 + z = 11.916375288 + -11 z = 11.916375288 + -11 Combine like terms: 11.916375288 + -11 = 0.916375288 z = 0.916375288 Simplifying z = 0.916375288Subproblem 2
z + 11 = -11.916375288 Simplifying z + 11 = -11.916375288 Reorder the terms: 11 + z = -11.916375288 Solving 11 + z = -11.916375288 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 = -11.916375288 + -11 Combine like terms: 11 + -11 = 0 0 + z = -11.916375288 + -11 z = -11.916375288 + -11 Combine like terms: -11.916375288 + -11 = -22.916375288 z = -22.916375288 Simplifying z = -22.916375288Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.916375288, -22.916375288}
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