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Simplifying x6 + -3x3 + -3 = 0 Reorder the terms: -3 + -3x3 + x6 = 0 Solving -3 + -3x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -3x3 + 3 + x6 = 0 + 3 Reorder the terms: -3 + 3 + -3x3 + x6 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3x3 + x6 = 0 + 3 -3x3 + x6 = 0 + 3 Combine like terms: 0 + 3 = 3 -3x3 + x6 = 3 The x term is -3x3. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x3 + 2.25 + x6 = 3 + 2.25 Reorder the terms: 2.25 + -3x3 + x6 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3x3 + x6 = 5.25 Factor a perfect square on the left side: (x3 + -1.5)(x3 + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x3 + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x3 + -1.5 = 2.291287847 Simplifying x3 + -1.5 = 2.291287847 Reorder the terms: -1.5 + x3 = 2.291287847 Solving -1.5 + x3 = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x3 = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x3 = 2.291287847 + 1.5 x3 = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 x3 = 3.791287847 Simplifying x3 = 3.791287847 Reorder the terms: -3.791287847 + x3 = 3.791287847 + -3.791287847 Combine like terms: 3.791287847 + -3.791287847 = 0.000000000 -3.791287847 + 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 + -1.5 = -2.291287847 Simplifying x3 + -1.5 = -2.291287847 Reorder the terms: -1.5 + x3 = -2.291287847 Solving -1.5 + x3 = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x3 = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x3 = -2.291287847 + 1.5 x3 = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 x3 = -0.791287847 Simplifying x3 = -0.791287847 Reorder the terms: 0.791287847 + x3 = -0.791287847 + 0.791287847 Combine like terms: -0.791287847 + 0.791287847 = 0.000000000 0.791287847 + 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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