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Simplifying z2 + -22z = 24 Reorder the terms: -22z + z2 = 24 Solving -22z + z2 = 24 Solving for variable 'z'. Reorder the terms: -24 + -22z + z2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -22z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -22z + 24 + z2 = 0 + 24 Reorder the terms: -24 + 24 + -22z + z2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -22z + z2 = 0 + 24 -22z + z2 = 0 + 24 Combine like terms: 0 + 24 = 24 -22z + z2 = 24 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 = 24 + 121 Reorder the terms: 121 + -22z + z2 = 24 + 121 Combine like terms: 24 + 121 = 145 121 + -22z + z2 = 145 Factor a perfect square on the left side: (z + -11)(z + -11) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (z + -11) equal to 12.041594579 and -12.041594579.Subproblem 1
z + -11 = 12.041594579 Simplifying z + -11 = 12.041594579 Reorder the terms: -11 + z = 12.041594579 Solving -11 + z = 12.041594579 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 = 12.041594579 + 11 Combine like terms: -11 + 11 = 0 0 + z = 12.041594579 + 11 z = 12.041594579 + 11 Combine like terms: 12.041594579 + 11 = 23.041594579 z = 23.041594579 Simplifying z = 23.041594579Subproblem 2
z + -11 = -12.041594579 Simplifying z + -11 = -12.041594579 Reorder the terms: -11 + z = -12.041594579 Solving -11 + z = -12.041594579 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 = -12.041594579 + 11 Combine like terms: -11 + 11 = 0 0 + z = -12.041594579 + 11 z = -12.041594579 + 11 Combine like terms: -12.041594579 + 11 = -1.041594579 z = -1.041594579 Simplifying z = -1.041594579Solution
The solution to the problem is based on the solutions from the subproblems. z = {23.041594579, -1.041594579}
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