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Simplifying z2 + 11z + 14 = 0 Reorder the terms: 14 + 11z + z2 = 0 Solving 14 + 11z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 11z + -14 + z2 = 0 + -14 Reorder the terms: 14 + -14 + 11z + z2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 11z + z2 = 0 + -14 11z + z2 = 0 + -14 Combine like terms: 0 + -14 = -14 11z + z2 = -14 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 = -14 + 30.25 Reorder the terms: 30.25 + 11z + z2 = -14 + 30.25 Combine like terms: -14 + 30.25 = 16.25 30.25 + 11z + z2 = 16.25 Factor a perfect square on the left side: (z + 5.5)(z + 5.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (z + 5.5) equal to 4.031128874 and -4.031128874.Subproblem 1
z + 5.5 = 4.031128874 Simplifying z + 5.5 = 4.031128874 Reorder the terms: 5.5 + z = 4.031128874 Solving 5.5 + z = 4.031128874 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 = 4.031128874 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = 4.031128874 + -5.5 z = 4.031128874 + -5.5 Combine like terms: 4.031128874 + -5.5 = -1.468871126 z = -1.468871126 Simplifying z = -1.468871126Subproblem 2
z + 5.5 = -4.031128874 Simplifying z + 5.5 = -4.031128874 Reorder the terms: 5.5 + z = -4.031128874 Solving 5.5 + z = -4.031128874 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 = -4.031128874 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = -4.031128874 + -5.5 z = -4.031128874 + -5.5 Combine like terms: -4.031128874 + -5.5 = -9.531128874 z = -9.531128874 Simplifying z = -9.531128874Solution
The solution to the problem is based on the solutions from the subproblems. z = {-1.468871126, -9.531128874}
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