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Simplifying x6 + -14x3 + 1 = 0 Reorder the terms: 1 + -14x3 + x6 = 0 Solving 1 + -14x3 + 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 + -14x3 + -1 + x6 = 0 + -1 Reorder the terms: 1 + -1 + -14x3 + x6 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -14x3 + x6 = 0 + -1 -14x3 + x6 = 0 + -1 Combine like terms: 0 + -1 = -1 -14x3 + x6 = -1 The x term is -14x3. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x3 + 49 + x6 = -1 + 49 Reorder the terms: 49 + -14x3 + x6 = -1 + 49 Combine like terms: -1 + 49 = 48 49 + -14x3 + x6 = 48 Factor a perfect square on the left side: (x3 + -7)(x3 + -7) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x3 + -7) equal to 6.92820323 and -6.92820323.Subproblem 1
x3 + -7 = 6.92820323 Simplifying x3 + -7 = 6.92820323 Reorder the terms: -7 + x3 = 6.92820323 Solving -7 + x3 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x3 = 6.92820323 + 7 Combine like terms: -7 + 7 = 0 0 + x3 = 6.92820323 + 7 x3 = 6.92820323 + 7 Combine like terms: 6.92820323 + 7 = 13.92820323 x3 = 13.92820323 Simplifying x3 = 13.92820323 Reorder the terms: -13.92820323 + x3 = 13.92820323 + -13.92820323 Combine like terms: 13.92820323 + -13.92820323 = 0.00000000 -13.92820323 + x3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + -7 = -6.92820323 Simplifying x3 + -7 = -6.92820323 Reorder the terms: -7 + x3 = -6.92820323 Solving -7 + x3 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x3 = -6.92820323 + 7 Combine like terms: -7 + 7 = 0 0 + x3 = -6.92820323 + 7 x3 = -6.92820323 + 7 Combine like terms: -6.92820323 + 7 = 0.07179677 x3 = 0.07179677 Simplifying x3 = 0.07179677 Reorder the terms: -0.07179677 + x3 = 0.07179677 + -0.07179677 Combine like terms: 0.07179677 + -0.07179677 = 0.00000000 -0.07179677 + x3 = 0.00000000 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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