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Simplifying z2 + -8z = -13 Reorder the terms: -8z + z2 = -13 Solving -8z + z2 = -13 Solving for variable 'z'. Reorder the terms: 13 + -8z + z2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8z + -13 + z2 = 0 + -13 Reorder the terms: 13 + -13 + -8z + z2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8z + z2 = 0 + -13 -8z + z2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8z + z2 = -13 The z term is -8z. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8z + 16 + z2 = -13 + 16 Reorder the terms: 16 + -8z + z2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8z + z2 = 3 Factor a perfect square on the left side: (z + -4)(z + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (z + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
z + -4 = 1.732050808 Simplifying z + -4 = 1.732050808 Reorder the terms: -4 + z = 1.732050808 Solving -4 + z = 1.732050808 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + z = 1.732050808 + 4 z = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 z = 5.732050808 Simplifying z = 5.732050808Subproblem 2
z + -4 = -1.732050808 Simplifying z + -4 = -1.732050808 Reorder the terms: -4 + z = -1.732050808 Solving -4 + z = -1.732050808 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + z = -1.732050808 + 4 z = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 z = 2.267949192 Simplifying z = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. z = {5.732050808, 2.267949192}
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