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Simplifying x = 3x2 + 2x + -48 Reorder the terms: x = -48 + 2x + 3x2 Solving x = -48 + 2x + 3x2 Solving for variable 'x'. Reorder the terms: 48 + x + -2x + -3x2 = -48 + 2x + 3x2 + 48 + -2x + -3x2 Combine like terms: x + -2x = -1x 48 + -1x + -3x2 = -48 + 2x + 3x2 + 48 + -2x + -3x2 Reorder the terms: 48 + -1x + -3x2 = -48 + 48 + 2x + -2x + 3x2 + -3x2 Combine like terms: -48 + 48 = 0 48 + -1x + -3x2 = 0 + 2x + -2x + 3x2 + -3x2 48 + -1x + -3x2 = 2x + -2x + 3x2 + -3x2 Combine like terms: 2x + -2x = 0 48 + -1x + -3x2 = 0 + 3x2 + -3x2 48 + -1x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 48 + -1x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -16 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.3333333333x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 0.3333333333x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.3333333333x + x2 = 0 + 16 0.3333333333x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 0.3333333333x + x2 = 16 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 16 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 16 + 0.02777777779 Combine like terms: 16 + 0.02777777779 = 16.02777777779 0.02777777779 + 0.3333333333x + x2 = 16.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 16.02777777779 Calculate the square root of the right side: 4.003470716 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 4.003470716 and -4.003470716.Subproblem 1
x + 0.1666666667 = 4.003470716 Simplifying x + 0.1666666667 = 4.003470716 Reorder the terms: 0.1666666667 + x = 4.003470716 Solving 0.1666666667 + x = 4.003470716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 4.003470716 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 4.003470716 + -0.1666666667 x = 4.003470716 + -0.1666666667 Combine like terms: 4.003470716 + -0.1666666667 = 3.8368040493 x = 3.8368040493 Simplifying x = 3.8368040493Subproblem 2
x + 0.1666666667 = -4.003470716 Simplifying x + 0.1666666667 = -4.003470716 Reorder the terms: 0.1666666667 + x = -4.003470716 Solving 0.1666666667 + x = -4.003470716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -4.003470716 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -4.003470716 + -0.1666666667 x = -4.003470716 + -0.1666666667 Combine like terms: -4.003470716 + -0.1666666667 = -4.1701373827 x = -4.1701373827 Simplifying x = -4.1701373827Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8368040493, -4.1701373827}
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