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Simplifying 6x8 + -24x4 + 2 = 0 Reorder the terms: 2 + -24x4 + 6x8 = 0 Solving 2 + -24x4 + 6x8 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -12x4 + 3x8) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -12x4 + 3x8)' equal to zero and attempt to solve: Simplifying 1 + -12x4 + 3x8 = 0 Solving 1 + -12x4 + 3x8 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -4x4 + x8 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -4x4 + -0.3333333333 + x8 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -4x4 + x8 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -4x4 + x8 = 0 + -0.3333333333 -4x4 + x8 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -4x4 + x8 = -0.3333333333 The x term is -4x4. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x4 + 4 + x8 = -0.3333333333 + 4 Reorder the terms: 4 + -4x4 + x8 = -0.3333333333 + 4 Combine like terms: -0.3333333333 + 4 = 3.6666666667 4 + -4x4 + x8 = 3.6666666667 Factor a perfect square on the left side: (x4 + -2)(x4 + -2) = 3.6666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x4 + -2) equal to 1.914854216 and -1.914854216.Subproblem 1
x4 + -2 = 1.914854216 Simplifying x4 + -2 = 1.914854216 Reorder the terms: -2 + x4 = 1.914854216 Solving -2 + x4 = 1.914854216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x4 = 1.914854216 + 2 Combine like terms: -2 + 2 = 0 0 + x4 = 1.914854216 + 2 x4 = 1.914854216 + 2 Combine like terms: 1.914854216 + 2 = 3.914854216 x4 = 3.914854216 Simplifying x4 = 3.914854216 Reorder the terms: -3.914854216 + x4 = 3.914854216 + -3.914854216 Combine like terms: 3.914854216 + -3.914854216 = 0.000000000 -3.914854216 + x4 = 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
x4 + -2 = -1.914854216 Simplifying x4 + -2 = -1.914854216 Reorder the terms: -2 + x4 = -1.914854216 Solving -2 + x4 = -1.914854216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x4 = -1.914854216 + 2 Combine like terms: -2 + 2 = 0 0 + x4 = -1.914854216 + 2 x4 = -1.914854216 + 2 Combine like terms: -1.914854216 + 2 = 0.085145784 x4 = 0.085145784 Simplifying x4 = 0.085145784 Reorder the terms: -0.085145784 + x4 = 0.085145784 + -0.085145784 Combine like terms: 0.085145784 + -0.085145784 = 0.000000000 -0.085145784 + x4 = 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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