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Simplifying 4x6 + -24x3 + -35 = 0 Reorder the terms: -35 + -24x3 + 4x6 = 0 Solving -35 + -24x3 + 4x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -6x3 + x6 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -6x3 + 8.75 + x6 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -6x3 + x6 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -6x3 + x6 = 0 + 8.75 -6x3 + x6 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -6x3 + x6 = 8.75 The x term is -6x3. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x3 + 9 + x6 = 8.75 + 9 Reorder the terms: 9 + -6x3 + x6 = 8.75 + 9 Combine like terms: 8.75 + 9 = 17.75 9 + -6x3 + x6 = 17.75 Factor a perfect square on the left side: (x3 + -3)(x3 + -3) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x3 + -3) equal to 4.213074887 and -4.213074887.Subproblem 1
x3 + -3 = 4.213074887 Simplifying x3 + -3 = 4.213074887 Reorder the terms: -3 + x3 = 4.213074887 Solving -3 + x3 = 4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x3 = 4.213074887 + 3 Combine like terms: -3 + 3 = 0 0 + x3 = 4.213074887 + 3 x3 = 4.213074887 + 3 Combine like terms: 4.213074887 + 3 = 7.213074887 x3 = 7.213074887 Simplifying x3 = 7.213074887 Reorder the terms: -7.213074887 + x3 = 7.213074887 + -7.213074887 Combine like terms: 7.213074887 + -7.213074887 = 0.000000000 -7.213074887 + 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 = -4.213074887 Simplifying x3 + -3 = -4.213074887 Reorder the terms: -3 + x3 = -4.213074887 Solving -3 + x3 = -4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x3 = -4.213074887 + 3 Combine like terms: -3 + 3 = 0 0 + x3 = -4.213074887 + 3 x3 = -4.213074887 + 3 Combine like terms: -4.213074887 + 3 = -1.213074887 x3 = -1.213074887 Simplifying x3 = -1.213074887 Reorder the terms: 1.213074887 + x3 = -1.213074887 + 1.213074887 Combine like terms: -1.213074887 + 1.213074887 = 0.000000000 1.213074887 + 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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