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Simplifying (-1x)(-2 + -3x) + -1x = -3(-2 + -3) Remove parenthesis around (-1x) -1x(-2 + -3x) + -1x = -3(-2 + -3) (-2 * -1x + -3x * -1x) + -1x = -3(-2 + -3) (2x + 3x2) + -1x = -3(-2 + -3) Reorder the terms: 2x + -1x + 3x2 = -3(-2 + -3) Combine like terms: 2x + -1x = 1x 1x + 3x2 = -3(-2 + -3) Combine like terms: -2 + -3 = -5 1x + 3x2 = -3(-5) Multiply -3 * -5 1x + 3x2 = 15 Solving 1x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 1x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.3333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.3333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.3333333333x + x2 = 0 + 5 0.3333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.3333333333x + x2 = 5 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 = 5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 5 + 0.02777777779 Combine like terms: 5 + 0.02777777779 = 5.02777777779 0.02777777779 + 0.3333333333x + x2 = 5.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 5.02777777779 Calculate the square root of the right side: 2.242270675 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 2.242270675 and -2.242270675.Subproblem 1
x + 0.1666666667 = 2.242270675 Simplifying x + 0.1666666667 = 2.242270675 Reorder the terms: 0.1666666667 + x = 2.242270675 Solving 0.1666666667 + x = 2.242270675 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 = 2.242270675 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 2.242270675 + -0.1666666667 x = 2.242270675 + -0.1666666667 Combine like terms: 2.242270675 + -0.1666666667 = 2.0756040083 x = 2.0756040083 Simplifying x = 2.0756040083Subproblem 2
x + 0.1666666667 = -2.242270675 Simplifying x + 0.1666666667 = -2.242270675 Reorder the terms: 0.1666666667 + x = -2.242270675 Solving 0.1666666667 + x = -2.242270675 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 = -2.242270675 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -2.242270675 + -0.1666666667 x = -2.242270675 + -0.1666666667 Combine like terms: -2.242270675 + -0.1666666667 = -2.4089373417 x = -2.4089373417 Simplifying x = -2.4089373417Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0756040083, -2.4089373417}
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