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Simplifying z2 + -49z + 8 = 0 Reorder the terms: 8 + -49z + z2 = 0 Solving 8 + -49z + 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 + -49z + -8 + z2 = 0 + -8 Reorder the terms: 8 + -8 + -49z + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -49z + z2 = 0 + -8 -49z + z2 = 0 + -8 Combine like terms: 0 + -8 = -8 -49z + z2 = -8 The z term is -49z. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49z + 600.25 + z2 = -8 + 600.25 Reorder the terms: 600.25 + -49z + z2 = -8 + 600.25 Combine like terms: -8 + 600.25 = 592.25 600.25 + -49z + z2 = 592.25 Factor a perfect square on the left side: (z + -24.5)(z + -24.5) = 592.25 Calculate the square root of the right side: 24.336187047 Break this problem into two subproblems by setting (z + -24.5) equal to 24.336187047 and -24.336187047.Subproblem 1
z + -24.5 = 24.336187047 Simplifying z + -24.5 = 24.336187047 Reorder the terms: -24.5 + z = 24.336187047 Solving -24.5 + z = 24.336187047 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + z = 24.336187047 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + z = 24.336187047 + 24.5 z = 24.336187047 + 24.5 Combine like terms: 24.336187047 + 24.5 = 48.836187047 z = 48.836187047 Simplifying z = 48.836187047Subproblem 2
z + -24.5 = -24.336187047 Simplifying z + -24.5 = -24.336187047 Reorder the terms: -24.5 + z = -24.336187047 Solving -24.5 + z = -24.336187047 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + z = -24.336187047 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + z = -24.336187047 + 24.5 z = -24.336187047 + 24.5 Combine like terms: -24.336187047 + 24.5 = 0.163812953 z = 0.163812953 Simplifying z = 0.163812953Solution
The solution to the problem is based on the solutions from the subproblems. z = {48.836187047, 0.163812953}
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