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Simplifying x8 + 100x4 + -10000 = 0 Reorder the terms: -10000 + 100x4 + x8 = 0 Solving -10000 + 100x4 + x8 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 100x4 + 10000 + x8 = 0 + 10000 Reorder the terms: -10000 + 10000 + 100x4 + x8 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 100x4 + x8 = 0 + 10000 100x4 + x8 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 100x4 + x8 = 10000 The x term is 100x4. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x4 + 2500 + x8 = 10000 + 2500 Reorder the terms: 2500 + 100x4 + x8 = 10000 + 2500 Combine like terms: 10000 + 2500 = 12500 2500 + 100x4 + x8 = 12500 Factor a perfect square on the left side: (x4 + 50)(x4 + 50) = 12500 Calculate the square root of the right side: 111.803398875 Break this problem into two subproblems by setting (x4 + 50) equal to 111.803398875 and -111.803398875.Subproblem 1
x4 + 50 = 111.803398875 Simplifying x4 + 50 = 111.803398875 Reorder the terms: 50 + x4 = 111.803398875 Solving 50 + x4 = 111.803398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x4 = 111.803398875 + -50 Combine like terms: 50 + -50 = 0 0 + x4 = 111.803398875 + -50 x4 = 111.803398875 + -50 Combine like terms: 111.803398875 + -50 = 61.803398875 x4 = 61.803398875 Simplifying x4 = 61.803398875 Reorder the terms: -61.803398875 + x4 = 61.803398875 + -61.803398875 Combine like terms: 61.803398875 + -61.803398875 = 0.000000000 -61.803398875 + x4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x4 + 50 = -111.803398875 Simplifying x4 + 50 = -111.803398875 Reorder the terms: 50 + x4 = -111.803398875 Solving 50 + x4 = -111.803398875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x4 = -111.803398875 + -50 Combine like terms: 50 + -50 = 0 0 + x4 = -111.803398875 + -50 x4 = -111.803398875 + -50 Combine like terms: -111.803398875 + -50 = -161.803398875 x4 = -161.803398875 Simplifying x4 = -161.803398875 Reorder the terms: 161.803398875 + x4 = -161.803398875 + 161.803398875 Combine like terms: -161.803398875 + 161.803398875 = 0.000000000 161.803398875 + x4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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