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Simplifying x6 + -10x3 + 6 = 0 Reorder the terms: 6 + -10x3 + x6 = 0 Solving 6 + -10x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -10x3 + -6 + x6 = 0 + -6 Reorder the terms: 6 + -6 + -10x3 + x6 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -10x3 + x6 = 0 + -6 -10x3 + x6 = 0 + -6 Combine like terms: 0 + -6 = -6 -10x3 + x6 = -6 The x term is -10x3. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x3 + 25 + x6 = -6 + 25 Reorder the terms: 25 + -10x3 + x6 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + -10x3 + x6 = 19 Factor a perfect square on the left side: (x3 + -5)(x3 + -5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x3 + -5) equal to 4.358898944 and -4.358898944.Subproblem 1
x3 + -5 = 4.358898944 Simplifying x3 + -5 = 4.358898944 Reorder the terms: -5 + x3 = 4.358898944 Solving -5 + x3 = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x3 = 4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + x3 = 4.358898944 + 5 x3 = 4.358898944 + 5 Combine like terms: 4.358898944 + 5 = 9.358898944 x3 = 9.358898944 Simplifying x3 = 9.358898944 Reorder the terms: -9.358898944 + x3 = 9.358898944 + -9.358898944 Combine like terms: 9.358898944 + -9.358898944 = 0.000000000 -9.358898944 + 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 + -5 = -4.358898944 Simplifying x3 + -5 = -4.358898944 Reorder the terms: -5 + x3 = -4.358898944 Solving -5 + x3 = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x3 = -4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + x3 = -4.358898944 + 5 x3 = -4.358898944 + 5 Combine like terms: -4.358898944 + 5 = 0.641101056 x3 = 0.641101056 Simplifying x3 = 0.641101056 Reorder the terms: -0.641101056 + x3 = 0.641101056 + -0.641101056 Combine like terms: 0.641101056 + -0.641101056 = 0.000000000 -0.641101056 + 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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