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Simplifying 8x6 + -16x3 + -1 = 0 Reorder the terms: -1 + -16x3 + 8x6 = 0 Solving -1 + -16x3 + 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 + -2x3 + x6 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -2x3 + 0.125 + x6 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -2x3 + x6 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -2x3 + x6 = 0 + 0.125 -2x3 + x6 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -2x3 + x6 = 0.125 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 = 0.125 + 1 Reorder the terms: 1 + -2x3 + x6 = 0.125 + 1 Combine like terms: 0.125 + 1 = 1.125 1 + -2x3 + x6 = 1.125 Factor a perfect square on the left side: (x3 + -1)(x3 + -1) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (x3 + -1) equal to 1.060660172 and -1.060660172.Subproblem 1
x3 + -1 = 1.060660172 Simplifying x3 + -1 = 1.060660172 Reorder the terms: -1 + x3 = 1.060660172 Solving -1 + x3 = 1.060660172 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 = 1.060660172 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = 1.060660172 + 1 x3 = 1.060660172 + 1 Combine like terms: 1.060660172 + 1 = 2.060660172 x3 = 2.060660172 Simplifying x3 = 2.060660172 Reorder the terms: -2.060660172 + x3 = 2.060660172 + -2.060660172 Combine like terms: 2.060660172 + -2.060660172 = 0.000000000 -2.060660172 + 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 = -1.060660172 Simplifying x3 + -1 = -1.060660172 Reorder the terms: -1 + x3 = -1.060660172 Solving -1 + x3 = -1.060660172 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 = -1.060660172 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = -1.060660172 + 1 x3 = -1.060660172 + 1 Combine like terms: -1.060660172 + 1 = -0.060660172 x3 = -0.060660172 Simplifying x3 = -0.060660172 Reorder the terms: 0.060660172 + x3 = -0.060660172 + 0.060660172 Combine like terms: -0.060660172 + 0.060660172 = 0.000000000 0.060660172 + 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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