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Simplifying 16x6 + -8x3 + -7 = 0 Reorder the terms: -7 + -8x3 + 16x6 = 0 Solving -7 + -8x3 + 16x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + -0.5x3 + x6 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -0.5x3 + 0.4375 + x6 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -0.5x3 + x6 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -0.5x3 + x6 = 0 + 0.4375 -0.5x3 + x6 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -0.5x3 + x6 = 0.4375 The x term is -0.5x3. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x3 + 0.0625 + x6 = 0.4375 + 0.0625 Reorder the terms: 0.0625 + -0.5x3 + x6 = 0.4375 + 0.0625 Combine like terms: 0.4375 + 0.0625 = 0.5 0.0625 + -0.5x3 + x6 = 0.5 Factor a perfect square on the left side: (x3 + -0.25)(x3 + -0.25) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x3 + -0.25) equal to 0.707106781 and -0.707106781.Subproblem 1
x3 + -0.25 = 0.707106781 Simplifying x3 + -0.25 = 0.707106781 Reorder the terms: -0.25 + x3 = 0.707106781 Solving -0.25 + x3 = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x3 = 0.707106781 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x3 = 0.707106781 + 0.25 x3 = 0.707106781 + 0.25 Combine like terms: 0.707106781 + 0.25 = 0.957106781 x3 = 0.957106781 Simplifying x3 = 0.957106781 Reorder the terms: -0.957106781 + x3 = 0.957106781 + -0.957106781 Combine like terms: 0.957106781 + -0.957106781 = 0.000000000 -0.957106781 + 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 + -0.25 = -0.707106781 Simplifying x3 + -0.25 = -0.707106781 Reorder the terms: -0.25 + x3 = -0.707106781 Solving -0.25 + x3 = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x3 = -0.707106781 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x3 = -0.707106781 + 0.25 x3 = -0.707106781 + 0.25 Combine like terms: -0.707106781 + 0.25 = -0.457106781 x3 = -0.457106781 Simplifying x3 = -0.457106781 Reorder the terms: 0.457106781 + x3 = -0.457106781 + 0.457106781 Combine like terms: -0.457106781 + 0.457106781 = 0.000000000 0.457106781 + 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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