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Simplifying 0 = 5x6 + -8x3 + -2 Reorder the terms: 0 = -2 + -8x3 + 5x6 Solving 0 = -2 + -8x3 + 5x6 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + 8x3 + -5x6 = -2 + -8x3 + 5x6 + 2 + 8x3 + -5x6 Reorder the terms: 2 + 8x3 + -5x6 = -2 + 2 + -8x3 + 8x3 + 5x6 + -5x6 Combine like terms: -2 + 2 = 0 2 + 8x3 + -5x6 = 0 + -8x3 + 8x3 + 5x6 + -5x6 2 + 8x3 + -5x6 = -8x3 + 8x3 + 5x6 + -5x6 Combine like terms: -8x3 + 8x3 = 0 2 + 8x3 + -5x6 = 0 + 5x6 + -5x6 2 + 8x3 + -5x6 = 5x6 + -5x6 Combine like terms: 5x6 + -5x6 = 0 2 + 8x3 + -5x6 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -1.6x3 + x6 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.6x3 + 0.4 + x6 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.6x3 + x6 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.6x3 + x6 = 0 + 0.4 -1.6x3 + x6 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.6x3 + x6 = 0.4 The x term is -1.6x3. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x3 + 0.64 + x6 = 0.4 + 0.64 Reorder the terms: 0.64 + -1.6x3 + x6 = 0.4 + 0.64 Combine like terms: 0.4 + 0.64 = 1.04 0.64 + -1.6x3 + x6 = 1.04 Factor a perfect square on the left side: (x3 + -0.8)(x3 + -0.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x3 + -0.8) equal to 1.019803903 and -1.019803903.Subproblem 1
x3 + -0.8 = 1.019803903 Simplifying x3 + -0.8 = 1.019803903 Reorder the terms: -0.8 + x3 = 1.019803903 Solving -0.8 + x3 = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x3 = 1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x3 = 1.019803903 + 0.8 x3 = 1.019803903 + 0.8 Combine like terms: 1.019803903 + 0.8 = 1.819803903 x3 = 1.819803903 Simplifying x3 = 1.819803903 Reorder the terms: -1.819803903 + x3 = 1.819803903 + -1.819803903 Combine like terms: 1.819803903 + -1.819803903 = 0.000000000 -1.819803903 + 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 + -0.8 = -1.019803903 Simplifying x3 + -0.8 = -1.019803903 Reorder the terms: -0.8 + x3 = -1.019803903 Solving -0.8 + x3 = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x3 = -1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x3 = -1.019803903 + 0.8 x3 = -1.019803903 + 0.8 Combine like terms: -1.019803903 + 0.8 = -0.219803903 x3 = -0.219803903 Simplifying x3 = -0.219803903 Reorder the terms: 0.219803903 + x3 = -0.219803903 + 0.219803903 Combine like terms: -0.219803903 + 0.219803903 = 0.000000000 0.219803903 + 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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