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Simplifying z2 + -5z + -27 = 0 Reorder the terms: -27 + -5z + z2 = 0 Solving -27 + -5z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -5z + 27 + z2 = 0 + 27 Reorder the terms: -27 + 27 + -5z + z2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -5z + z2 = 0 + 27 -5z + z2 = 0 + 27 Combine like terms: 0 + 27 = 27 -5z + z2 = 27 The z term is -5z. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5z + 6.25 + z2 = 27 + 6.25 Reorder the terms: 6.25 + -5z + z2 = 27 + 6.25 Combine like terms: 27 + 6.25 = 33.25 6.25 + -5z + z2 = 33.25 Factor a perfect square on the left side: (z + -2.5)(z + -2.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (z + -2.5) equal to 5.766281297 and -5.766281297.Subproblem 1
z + -2.5 = 5.766281297 Simplifying z + -2.5 = 5.766281297 Reorder the terms: -2.5 + z = 5.766281297 Solving -2.5 + z = 5.766281297 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = 5.766281297 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = 5.766281297 + 2.5 z = 5.766281297 + 2.5 Combine like terms: 5.766281297 + 2.5 = 8.266281297 z = 8.266281297 Simplifying z = 8.266281297Subproblem 2
z + -2.5 = -5.766281297 Simplifying z + -2.5 = -5.766281297 Reorder the terms: -2.5 + z = -5.766281297 Solving -2.5 + z = -5.766281297 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = -5.766281297 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = -5.766281297 + 2.5 z = -5.766281297 + 2.5 Combine like terms: -5.766281297 + 2.5 = -3.266281297 z = -3.266281297 Simplifying z = -3.266281297Solution
The solution to the problem is based on the solutions from the subproblems. z = {8.266281297, -3.266281297}
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