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Simplifying 8x6 = 6x3 + 7 Reorder the terms: 8x6 = 7 + 6x3 Solving 8x6 = 7 + 6x3 Solving for variable 'x'. Reorder the terms: -7 + -6x3 + 8x6 = 7 + 6x3 + -7 + -6x3 Reorder the terms: -7 + -6x3 + 8x6 = 7 + -7 + 6x3 + -6x3 Combine like terms: 7 + -7 = 0 -7 + -6x3 + 8x6 = 0 + 6x3 + -6x3 -7 + -6x3 + 8x6 = 6x3 + -6x3 Combine like terms: 6x3 + -6x3 = 0 -7 + -6x3 + 8x6 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.75x3 + x6 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.75x3 + 0.875 + x6 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.75x3 + x6 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.75x3 + x6 = 0 + 0.875 -0.75x3 + x6 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.75x3 + x6 = 0.875 The x term is -0.75x3. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x3 + 0.140625 + x6 = 0.875 + 0.140625 Reorder the terms: 0.140625 + -0.75x3 + x6 = 0.875 + 0.140625 Combine like terms: 0.875 + 0.140625 = 1.015625 0.140625 + -0.75x3 + x6 = 1.015625 Factor a perfect square on the left side: (x3 + -0.375)(x3 + -0.375) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x3 + -0.375) equal to 1.007782219 and -1.007782219.Subproblem 1
x3 + -0.375 = 1.007782219 Simplifying x3 + -0.375 = 1.007782219 Reorder the terms: -0.375 + x3 = 1.007782219 Solving -0.375 + x3 = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x3 = 1.007782219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x3 = 1.007782219 + 0.375 x3 = 1.007782219 + 0.375 Combine like terms: 1.007782219 + 0.375 = 1.382782219 x3 = 1.382782219 Simplifying x3 = 1.382782219 Reorder the terms: -1.382782219 + x3 = 1.382782219 + -1.382782219 Combine like terms: 1.382782219 + -1.382782219 = 0.000000000 -1.382782219 + 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 + -0.375 = -1.007782219 Simplifying x3 + -0.375 = -1.007782219 Reorder the terms: -0.375 + x3 = -1.007782219 Solving -0.375 + x3 = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x3 = -1.007782219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x3 = -1.007782219 + 0.375 x3 = -1.007782219 + 0.375 Combine like terms: -1.007782219 + 0.375 = -0.632782219 x3 = -0.632782219 Simplifying x3 = -0.632782219 Reorder the terms: 0.632782219 + x3 = -0.632782219 + 0.632782219 Combine like terms: -0.632782219 + 0.632782219 = 0.000000000 0.632782219 + 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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