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Simplifying z2 + -6z + -2 = 0 Reorder the terms: -2 + -6z + z2 = 0 Solving -2 + -6z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -6z + 2 + z2 = 0 + 2 Reorder the terms: -2 + 2 + -6z + z2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6z + z2 = 0 + 2 -6z + z2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6z + z2 = 2 The z term is -6z. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6z + 9 + z2 = 2 + 9 Reorder the terms: 9 + -6z + z2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + -6z + z2 = 11 Factor a perfect square on the left side: (z + -3)(z + -3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (z + -3) equal to 3.31662479 and -3.31662479.Subproblem 1
z + -3 = 3.31662479 Simplifying z + -3 = 3.31662479 Reorder the terms: -3 + z = 3.31662479 Solving -3 + z = 3.31662479 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = 3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + z = 3.31662479 + 3 z = 3.31662479 + 3 Combine like terms: 3.31662479 + 3 = 6.31662479 z = 6.31662479 Simplifying z = 6.31662479Subproblem 2
z + -3 = -3.31662479 Simplifying z + -3 = -3.31662479 Reorder the terms: -3 + z = -3.31662479 Solving -3 + z = -3.31662479 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = -3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + z = -3.31662479 + 3 z = -3.31662479 + 3 Combine like terms: -3.31662479 + 3 = -0.31662479 z = -0.31662479 Simplifying z = -0.31662479Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.31662479, -0.31662479}
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