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Simplifying 4x6 + 8x3 + 2 = 0 Reorder the terms: 2 + 8x3 + 4x6 = 0 Solving 2 + 8x3 + 4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 4x3 + 2x6) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 4x3 + 2x6)' equal to zero and attempt to solve: Simplifying 1 + 4x3 + 2x6 = 0 Solving 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 = -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.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 = -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. 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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