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Simplifying z2 + -7z + -27 = 0 Reorder the terms: -27 + -7z + z2 = 0 Solving -27 + -7z + 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 + -7z + 27 + z2 = 0 + 27 Reorder the terms: -27 + 27 + -7z + z2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -7z + z2 = 0 + 27 -7z + z2 = 0 + 27 Combine like terms: 0 + 27 = 27 -7z + z2 = 27 The z term is -7z. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7z + 12.25 + z2 = 27 + 12.25 Reorder the terms: 12.25 + -7z + z2 = 27 + 12.25 Combine like terms: 27 + 12.25 = 39.25 12.25 + -7z + z2 = 39.25 Factor a perfect square on the left side: (z + -3.5)(z + -3.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (z + -3.5) equal to 6.264982043 and -6.264982043.Subproblem 1
z + -3.5 = 6.264982043 Simplifying z + -3.5 = 6.264982043 Reorder the terms: -3.5 + z = 6.264982043 Solving -3.5 + z = 6.264982043 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + z = 6.264982043 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + z = 6.264982043 + 3.5 z = 6.264982043 + 3.5 Combine like terms: 6.264982043 + 3.5 = 9.764982043 z = 9.764982043 Simplifying z = 9.764982043Subproblem 2
z + -3.5 = -6.264982043 Simplifying z + -3.5 = -6.264982043 Reorder the terms: -3.5 + z = -6.264982043 Solving -3.5 + z = -6.264982043 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + z = -6.264982043 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + z = -6.264982043 + 3.5 z = -6.264982043 + 3.5 Combine like terms: -6.264982043 + 3.5 = -2.764982043 z = -2.764982043 Simplifying z = -2.764982043Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.764982043, -2.764982043}
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