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Simplifying 6x6 + -9x3 + -2 = 0 Reorder the terms: -2 + -9x3 + 6x6 = 0 Solving -2 + -9x3 + 6x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.3333333333 + -1.5x3 + x6 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.5x3 + 0.3333333333 + x6 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.5x3 + x6 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.5x3 + x6 = 0 + 0.3333333333 -1.5x3 + x6 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.5x3 + x6 = 0.3333333333 The x term is -1.5x3. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x3 + 0.5625 + x6 = 0.3333333333 + 0.5625 Reorder the terms: 0.5625 + -1.5x3 + x6 = 0.3333333333 + 0.5625 Combine like terms: 0.3333333333 + 0.5625 = 0.8958333333 0.5625 + -1.5x3 + x6 = 0.8958333333 Factor a perfect square on the left side: (x3 + -0.75)(x3 + -0.75) = 0.8958333333 Calculate the square root of the right side: 0.946484724 Break this problem into two subproblems by setting (x3 + -0.75) equal to 0.946484724 and -0.946484724.Subproblem 1
x3 + -0.75 = 0.946484724 Simplifying x3 + -0.75 = 0.946484724 Reorder the terms: -0.75 + x3 = 0.946484724 Solving -0.75 + x3 = 0.946484724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x3 = 0.946484724 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x3 = 0.946484724 + 0.75 x3 = 0.946484724 + 0.75 Combine like terms: 0.946484724 + 0.75 = 1.696484724 x3 = 1.696484724 Simplifying x3 = 1.696484724 Reorder the terms: -1.696484724 + x3 = 1.696484724 + -1.696484724 Combine like terms: 1.696484724 + -1.696484724 = 0.000000000 -1.696484724 + 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 + -0.75 = -0.946484724 Simplifying x3 + -0.75 = -0.946484724 Reorder the terms: -0.75 + x3 = -0.946484724 Solving -0.75 + x3 = -0.946484724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x3 = -0.946484724 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x3 = -0.946484724 + 0.75 x3 = -0.946484724 + 0.75 Combine like terms: -0.946484724 + 0.75 = -0.196484724 x3 = -0.196484724 Simplifying x3 = -0.196484724 Reorder the terms: 0.196484724 + x3 = -0.196484724 + 0.196484724 Combine like terms: -0.196484724 + 0.196484724 = 0.000000000 0.196484724 + 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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