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Simplifying 2(x + -4) * 6x + 8 = x Reorder the terms: 2(-4 + x) * 6x + 8 = x Reorder the terms for easier multiplication: 2 * 6x(-4 + x) + 8 = x Multiply 2 * 6 12x(-4 + x) + 8 = x (-4 * 12x + x * 12x) + 8 = x (-48x + 12x2) + 8 = x Reorder the terms: 8 + -48x + 12x2 = x Solving 8 + -48x + 12x2 = x Solving for variable 'x'. Reorder the terms: 8 + -48x + -1x + 12x2 = x + -1x Combine like terms: -48x + -1x = -49x 8 + -49x + 12x2 = x + -1x Combine like terms: x + -1x = 0 8 + -49x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.6666666667 + -4.083333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -4.083333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -4.083333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -4.083333333x + x2 = 0 + -0.6666666667 -4.083333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -4.083333333x + x2 = -0.6666666667 The x term is -4.083333333x. Take half its coefficient (-2.041666667). Square it (4.168402779) and add it to both sides. Add '4.168402779' to each side of the equation. -4.083333333x + 4.168402779 + x2 = -0.6666666667 + 4.168402779 Reorder the terms: 4.168402779 + -4.083333333x + x2 = -0.6666666667 + 4.168402779 Combine like terms: -0.6666666667 + 4.168402779 = 3.5017361123 4.168402779 + -4.083333333x + x2 = 3.5017361123 Factor a perfect square on the left side: (x + -2.041666667)(x + -2.041666667) = 3.5017361123 Calculate the square root of the right side: 1.871292631 Break this problem into two subproblems by setting (x + -2.041666667) equal to 1.871292631 and -1.871292631.Subproblem 1
x + -2.041666667 = 1.871292631 Simplifying x + -2.041666667 = 1.871292631 Reorder the terms: -2.041666667 + x = 1.871292631 Solving -2.041666667 + x = 1.871292631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.041666667' to each side of the equation. -2.041666667 + 2.041666667 + x = 1.871292631 + 2.041666667 Combine like terms: -2.041666667 + 2.041666667 = 0.000000000 0.000000000 + x = 1.871292631 + 2.041666667 x = 1.871292631 + 2.041666667 Combine like terms: 1.871292631 + 2.041666667 = 3.912959298 x = 3.912959298 Simplifying x = 3.912959298Subproblem 2
x + -2.041666667 = -1.871292631 Simplifying x + -2.041666667 = -1.871292631 Reorder the terms: -2.041666667 + x = -1.871292631 Solving -2.041666667 + x = -1.871292631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.041666667' to each side of the equation. -2.041666667 + 2.041666667 + x = -1.871292631 + 2.041666667 Combine like terms: -2.041666667 + 2.041666667 = 0.000000000 0.000000000 + x = -1.871292631 + 2.041666667 x = -1.871292631 + 2.041666667 Combine like terms: -1.871292631 + 2.041666667 = 0.170374036 x = 0.170374036 Simplifying x = 0.170374036Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.912959298, 0.170374036}
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