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Simplifying x6 + -7x3 + -1 = 0 Reorder the terms: -1 + -7x3 + x6 = 0 Solving -1 + -7x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -7x3 + 1 + x6 = 0 + 1 Reorder the terms: -1 + 1 + -7x3 + x6 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7x3 + x6 = 0 + 1 -7x3 + x6 = 0 + 1 Combine like terms: 0 + 1 = 1 -7x3 + x6 = 1 The x term is -7x3. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x3 + 12.25 + x6 = 1 + 12.25 Reorder the terms: 12.25 + -7x3 + x6 = 1 + 12.25 Combine like terms: 1 + 12.25 = 13.25 12.25 + -7x3 + x6 = 13.25 Factor a perfect square on the left side: (x3 + -3.5)(x3 + -3.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x3 + -3.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x3 + -3.5 = 3.640054945 Simplifying x3 + -3.5 = 3.640054945 Reorder the terms: -3.5 + x3 = 3.640054945 Solving -3.5 + x3 = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x3 = 3.640054945 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x3 = 3.640054945 + 3.5 x3 = 3.640054945 + 3.5 Combine like terms: 3.640054945 + 3.5 = 7.140054945 x3 = 7.140054945 Simplifying x3 = 7.140054945 Reorder the terms: -7.140054945 + x3 = 7.140054945 + -7.140054945 Combine like terms: 7.140054945 + -7.140054945 = 0.000000000 -7.140054945 + x3 = 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
x3 + -3.5 = -3.640054945 Simplifying x3 + -3.5 = -3.640054945 Reorder the terms: -3.5 + x3 = -3.640054945 Solving -3.5 + x3 = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x3 = -3.640054945 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x3 = -3.640054945 + 3.5 x3 = -3.640054945 + 3.5 Combine like terms: -3.640054945 + 3.5 = -0.140054945 x3 = -0.140054945 Simplifying x3 = -0.140054945 Reorder the terms: 0.140054945 + x3 = -0.140054945 + 0.140054945 Combine like terms: -0.140054945 + 0.140054945 = 0.000000000 0.140054945 + x3 = 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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