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Simplifying z2 + 11z + -10 = 0 Reorder the terms: -10 + 11z + z2 = 0 Solving -10 + 11z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 11z + 10 + z2 = 0 + 10 Reorder the terms: -10 + 10 + 11z + z2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 11z + z2 = 0 + 10 11z + z2 = 0 + 10 Combine like terms: 0 + 10 = 10 11z + z2 = 10 The z term is 11z. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11z + 30.25 + z2 = 10 + 30.25 Reorder the terms: 30.25 + 11z + z2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + 11z + z2 = 40.25 Factor a perfect square on the left side: (z + 5.5)(z + 5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (z + 5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
z + 5.5 = 6.34428877 Simplifying z + 5.5 = 6.34428877 Reorder the terms: 5.5 + z = 6.34428877 Solving 5.5 + z = 6.34428877 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + z = 6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = 6.34428877 + -5.5 z = 6.34428877 + -5.5 Combine like terms: 6.34428877 + -5.5 = 0.84428877 z = 0.84428877 Simplifying z = 0.84428877Subproblem 2
z + 5.5 = -6.34428877 Simplifying z + 5.5 = -6.34428877 Reorder the terms: 5.5 + z = -6.34428877 Solving 5.5 + z = -6.34428877 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + z = -6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = -6.34428877 + -5.5 z = -6.34428877 + -5.5 Combine like terms: -6.34428877 + -5.5 = -11.84428877 z = -11.84428877 Simplifying z = -11.84428877Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.84428877, -11.84428877}
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