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Simplifying 8x6 + 5x3 + -1 = 0 Reorder the terms: -1 + 5x3 + 8x6 = 0 Solving -1 + 5x3 + 8x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + 0.625x3 + x6 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.625x3 + 0.125 + x6 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.625x3 + x6 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.625x3 + x6 = 0 + 0.125 0.625x3 + x6 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.625x3 + x6 = 0.125 The x term is 0.625x3. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x3 + 0.09765625 + x6 = 0.125 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x3 + x6 = 0.125 + 0.09765625 Combine like terms: 0.125 + 0.09765625 = 0.22265625 0.09765625 + 0.625x3 + x6 = 0.22265625 Factor a perfect square on the left side: (x3 + 0.3125)(x3 + 0.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x3 + 0.3125) equal to 0.471864652 and -0.471864652.Subproblem 1
x3 + 0.3125 = 0.471864652 Simplifying x3 + 0.3125 = 0.471864652 Reorder the terms: 0.3125 + x3 = 0.471864652 Solving 0.3125 + x3 = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x3 = 0.471864652 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x3 = 0.471864652 + -0.3125 x3 = 0.471864652 + -0.3125 Combine like terms: 0.471864652 + -0.3125 = 0.159364652 x3 = 0.159364652 Simplifying x3 = 0.159364652 Reorder the terms: -0.159364652 + x3 = 0.159364652 + -0.159364652 Combine like terms: 0.159364652 + -0.159364652 = 0.000000000 -0.159364652 + 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 + 0.3125 = -0.471864652 Simplifying x3 + 0.3125 = -0.471864652 Reorder the terms: 0.3125 + x3 = -0.471864652 Solving 0.3125 + x3 = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x3 = -0.471864652 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x3 = -0.471864652 + -0.3125 x3 = -0.471864652 + -0.3125 Combine like terms: -0.471864652 + -0.3125 = -0.784364652 x3 = -0.784364652 Simplifying x3 = -0.784364652 Reorder the terms: 0.784364652 + x3 = -0.784364652 + 0.784364652 Combine like terms: -0.784364652 + 0.784364652 = 0.000000000 0.784364652 + 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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