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Simplifying z2 + -8z + -10 = 0 Reorder the terms: -10 + -8z + z2 = 0 Solving -10 + -8z + 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 + -8z + 10 + z2 = 0 + 10 Reorder the terms: -10 + 10 + -8z + z2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8z + z2 = 0 + 10 -8z + z2 = 0 + 10 Combine like terms: 0 + 10 = 10 -8z + z2 = 10 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 = 10 + 16 Reorder the terms: 16 + -8z + z2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8z + z2 = 26 Factor a perfect square on the left side: (z + -4)(z + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (z + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
z + -4 = 5.099019514 Simplifying z + -4 = 5.099019514 Reorder the terms: -4 + z = 5.099019514 Solving -4 + z = 5.099019514 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 = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + z = 5.099019514 + 4 z = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 z = 9.099019514 Simplifying z = 9.099019514Subproblem 2
z + -4 = -5.099019514 Simplifying z + -4 = -5.099019514 Reorder the terms: -4 + z = -5.099019514 Solving -4 + z = -5.099019514 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 = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + z = -5.099019514 + 4 z = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 z = -1.099019514 Simplifying z = -1.099019514Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.099019514, -1.099019514}
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