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Simplifying z2 + -14z + 11 = 0 Reorder the terms: 11 + -14z + z2 = 0 Solving 11 + -14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -14z + -11 + z2 = 0 + -11 Reorder the terms: 11 + -11 + -14z + z2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -14z + z2 = 0 + -11 -14z + z2 = 0 + -11 Combine like terms: 0 + -11 = -11 -14z + z2 = -11 The z term is -14z. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14z + 49 + z2 = -11 + 49 Reorder the terms: 49 + -14z + z2 = -11 + 49 Combine like terms: -11 + 49 = 38 49 + -14z + z2 = 38 Factor a perfect square on the left side: (z + -7)(z + -7) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (z + -7) equal to 6.164414003 and -6.164414003.Subproblem 1
z + -7 = 6.164414003 Simplifying z + -7 = 6.164414003 Reorder the terms: -7 + z = 6.164414003 Solving -7 + z = 6.164414003 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + z = 6.164414003 + 7 z = 6.164414003 + 7 Combine like terms: 6.164414003 + 7 = 13.164414003 z = 13.164414003 Simplifying z = 13.164414003Subproblem 2
z + -7 = -6.164414003 Simplifying z + -7 = -6.164414003 Reorder the terms: -7 + z = -6.164414003 Solving -7 + z = -6.164414003 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + z = -6.164414003 + 7 z = -6.164414003 + 7 Combine like terms: -6.164414003 + 7 = 0.835585997 z = 0.835585997 Simplifying z = 0.835585997Solution
The solution to the problem is based on the solutions from the subproblems. z = {13.164414003, 0.835585997}
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