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Simplifying z2 + -2z + -13 = 0 Reorder the terms: -13 + -2z + z2 = 0 Solving -13 + -2z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -2z + 13 + z2 = 0 + 13 Reorder the terms: -13 + 13 + -2z + z2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2z + z2 = 0 + 13 -2z + z2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2z + z2 = 13 The z term is -2z. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2z + 1 + z2 = 13 + 1 Reorder the terms: 1 + -2z + z2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + -2z + z2 = 14 Factor a perfect square on the left side: (z + -1)(z + -1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (z + -1) equal to 3.741657387 and -3.741657387.Subproblem 1
z + -1 = 3.741657387 Simplifying z + -1 = 3.741657387 Reorder the terms: -1 + z = 3.741657387 Solving -1 + z = 3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + z = 3.741657387 + 1 z = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 z = 4.741657387 Simplifying z = 4.741657387Subproblem 2
z + -1 = -3.741657387 Simplifying z + -1 = -3.741657387 Reorder the terms: -1 + z = -3.741657387 Solving -1 + z = -3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + z = -3.741657387 + 1 z = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 z = -2.741657387 Simplifying z = -2.741657387Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.741657387, -2.741657387}
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