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Simplifying 3x3 + -3x6 + -9x3 + 5 = 0 Reorder the terms: 5 + 3x3 + -9x3 + -3x6 = 0 Combine like terms: 3x3 + -9x3 = -6x3 5 + -6x3 + -3x6 = 0 Solving 5 + -6x3 + -3x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + 2x3 + x6 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 2x3 + 1.666666667 + x6 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 2x3 + x6 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 2x3 + x6 = 0 + 1.666666667 2x3 + x6 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 2x3 + x6 = 1.666666667 The x term is 2x3. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x3 + 1 + x6 = 1.666666667 + 1 Reorder the terms: 1 + 2x3 + x6 = 1.666666667 + 1 Combine like terms: 1.666666667 + 1 = 2.666666667 1 + 2x3 + x6 = 2.666666667 Factor a perfect square on the left side: (x3 + 1)(x3 + 1) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (x3 + 1) equal to 1.632993162 and -1.632993162.Subproblem 1
x3 + 1 = 1.632993162 Simplifying x3 + 1 = 1.632993162 Reorder the terms: 1 + x3 = 1.632993162 Solving 1 + x3 = 1.632993162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x3 = 1.632993162 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = 1.632993162 + -1 x3 = 1.632993162 + -1 Combine like terms: 1.632993162 + -1 = 0.632993162 x3 = 0.632993162 Simplifying x3 = 0.632993162 Reorder the terms: -0.632993162 + x3 = 0.632993162 + -0.632993162 Combine like terms: 0.632993162 + -0.632993162 = 0.000000000 -0.632993162 + 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 = -1.632993162 Simplifying x3 + 1 = -1.632993162 Reorder the terms: 1 + x3 = -1.632993162 Solving 1 + x3 = -1.632993162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x3 = -1.632993162 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = -1.632993162 + -1 x3 = -1.632993162 + -1 Combine like terms: -1.632993162 + -1 = -2.632993162 x3 = -2.632993162 Simplifying x3 = -2.632993162 Reorder the terms: 2.632993162 + x3 = -2.632993162 + 2.632993162 Combine like terms: -2.632993162 + 2.632993162 = 0.000000000 2.632993162 + 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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