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Simplifying 0 = 2x6 + -4x3 + 1 Reorder the terms: 0 = 1 + -4x3 + 2x6 Solving 0 = 1 + -4x3 + 2x6 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 4x3 + -2x6 = 1 + -4x3 + 2x6 + -1 + 4x3 + -2x6 Reorder the terms: -1 + 4x3 + -2x6 = 1 + -1 + -4x3 + 4x3 + 2x6 + -2x6 Combine like terms: 1 + -1 = 0 -1 + 4x3 + -2x6 = 0 + -4x3 + 4x3 + 2x6 + -2x6 -1 + 4x3 + -2x6 = -4x3 + 4x3 + 2x6 + -2x6 Combine like terms: -4x3 + 4x3 = 0 -1 + 4x3 + -2x6 = 0 + 2x6 + -2x6 -1 + 4x3 + -2x6 = 2x6 + -2x6 Combine like terms: 2x6 + -2x6 = 0 -1 + 4x3 + -2x6 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -2x3 + x6 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2x3 + -0.5 + x6 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2x3 + x6 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2x3 + x6 = 0 + -0.5 -2x3 + x6 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2x3 + x6 = -0.5 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 = -0.5 + 1 Reorder the terms: 1 + -2x3 + x6 = -0.5 + 1 Combine like terms: -0.5 + 1 = 0.5 1 + -2x3 + x6 = 0.5 Factor a perfect square on the left side: (x3 + -1)(x3 + -1) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x3 + -1) equal to 0.707106781 and -0.707106781.Subproblem 1
x3 + -1 = 0.707106781 Simplifying x3 + -1 = 0.707106781 Reorder the terms: -1 + x3 = 0.707106781 Solving -1 + x3 = 0.707106781 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 = 0.707106781 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = 0.707106781 + 1 x3 = 0.707106781 + 1 Combine like terms: 0.707106781 + 1 = 1.707106781 x3 = 1.707106781 Simplifying x3 = 1.707106781 Reorder the terms: -1.707106781 + x3 = 1.707106781 + -1.707106781 Combine like terms: 1.707106781 + -1.707106781 = 0.000000000 -1.707106781 + 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 = -0.707106781 Simplifying x3 + -1 = -0.707106781 Reorder the terms: -1 + x3 = -0.707106781 Solving -1 + x3 = -0.707106781 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 = -0.707106781 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = -0.707106781 + 1 x3 = -0.707106781 + 1 Combine like terms: -0.707106781 + 1 = 0.292893219 x3 = 0.292893219 Simplifying x3 = 0.292893219 Reorder the terms: -0.292893219 + x3 = 0.292893219 + -0.292893219 Combine like terms: 0.292893219 + -0.292893219 = 0.000000000 -0.292893219 + 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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