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Simplifying z2 + -11z + 8 = 0 Reorder the terms: 8 + -11z + z2 = 0 Solving 8 + -11z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -11z + -8 + z2 = 0 + -8 Reorder the terms: 8 + -8 + -11z + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11z + z2 = 0 + -8 -11z + z2 = 0 + -8 Combine like terms: 0 + -8 = -8 -11z + z2 = -8 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 = -8 + 30.25 Reorder the terms: 30.25 + -11z + z2 = -8 + 30.25 Combine like terms: -8 + 30.25 = 22.25 30.25 + -11z + z2 = 22.25 Factor a perfect square on the left side: (z + -5.5)(z + -5.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (z + -5.5) equal to 4.716990566 and -4.716990566.Subproblem 1
z + -5.5 = 4.716990566 Simplifying z + -5.5 = 4.716990566 Reorder the terms: -5.5 + z = 4.716990566 Solving -5.5 + z = 4.716990566 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 = 4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = 4.716990566 + 5.5 z = 4.716990566 + 5.5 Combine like terms: 4.716990566 + 5.5 = 10.216990566 z = 10.216990566 Simplifying z = 10.216990566Subproblem 2
z + -5.5 = -4.716990566 Simplifying z + -5.5 = -4.716990566 Reorder the terms: -5.5 + z = -4.716990566 Solving -5.5 + z = -4.716990566 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 = -4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = -4.716990566 + 5.5 z = -4.716990566 + 5.5 Combine like terms: -4.716990566 + 5.5 = 0.783009434 z = 0.783009434 Simplifying z = 0.783009434Solution
The solution to the problem is based on the solutions from the subproblems. z = {10.216990566, 0.783009434}
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