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Simplifying 8x6 + 7x3 + 1 = 0 Reorder the terms: 1 + 7x3 + 8x6 = 0 Solving 1 + 7x3 + 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 + 0.875x3 + x6 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.875x3 + -0.125 + x6 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.875x3 + x6 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.875x3 + x6 = 0 + -0.125 0.875x3 + x6 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.875x3 + x6 = -0.125 The x term is 0.875x3. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x3 + 0.19140625 + x6 = -0.125 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x3 + x6 = -0.125 + 0.19140625 Combine like terms: -0.125 + 0.19140625 = 0.06640625 0.19140625 + 0.875x3 + x6 = 0.06640625 Factor a perfect square on the left side: (x3 + 0.4375)(x3 + 0.4375) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x3 + 0.4375) equal to 0.257694102 and -0.257694102.Subproblem 1
x3 + 0.4375 = 0.257694102 Simplifying x3 + 0.4375 = 0.257694102 Reorder the terms: 0.4375 + x3 = 0.257694102 Solving 0.4375 + x3 = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x3 = 0.257694102 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x3 = 0.257694102 + -0.4375 x3 = 0.257694102 + -0.4375 Combine like terms: 0.257694102 + -0.4375 = -0.179805898 x3 = -0.179805898 Simplifying x3 = -0.179805898 Reorder the terms: 0.179805898 + x3 = -0.179805898 + 0.179805898 Combine like terms: -0.179805898 + 0.179805898 = 0.000000000 0.179805898 + 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 + 0.4375 = -0.257694102 Simplifying x3 + 0.4375 = -0.257694102 Reorder the terms: 0.4375 + x3 = -0.257694102 Solving 0.4375 + x3 = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x3 = -0.257694102 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x3 = -0.257694102 + -0.4375 x3 = -0.257694102 + -0.4375 Combine like terms: -0.257694102 + -0.4375 = -0.695194102 x3 = -0.695194102 Simplifying x3 = -0.695194102 Reorder the terms: 0.695194102 + x3 = -0.695194102 + 0.695194102 Combine like terms: -0.695194102 + 0.695194102 = 0.000000000 0.695194102 + 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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