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Simplifying 2x + -3x(x + -4) = 2(3 + -2x) + 2 Reorder the terms: 2x + -3x(-4 + x) = 2(3 + -2x) + 2 2x + (-4 * -3x + x * -3x) = 2(3 + -2x) + 2 2x + (12x + -3x2) = 2(3 + -2x) + 2 Combine like terms: 2x + 12x = 14x 14x + -3x2 = 2(3 + -2x) + 2 14x + -3x2 = (3 * 2 + -2x * 2) + 2 14x + -3x2 = (6 + -4x) + 2 Reorder the terms: 14x + -3x2 = 6 + 2 + -4x Combine like terms: 6 + 2 = 8 14x + -3x2 = 8 + -4x Solving 14x + -3x2 = 8 + -4x Solving for variable 'x'. Reorder the terms: -8 + 14x + 4x + -3x2 = 8 + -4x + -8 + 4x Combine like terms: 14x + 4x = 18x -8 + 18x + -3x2 = 8 + -4x + -8 + 4x Reorder the terms: -8 + 18x + -3x2 = 8 + -8 + -4x + 4x Combine like terms: 8 + -8 = 0 -8 + 18x + -3x2 = 0 + -4x + 4x -8 + 18x + -3x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -8 + 18x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2.666666667 + -6x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -6x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -6x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + -2.666666667 -6x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -6x + x2 = -2.666666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -2.666666667 + 9 Reorder the terms: 9 + -6x + x2 = -2.666666667 + 9 Combine like terms: -2.666666667 + 9 = 6.333333333 9 + -6x + x2 = 6.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (x + -3) equal to 2.516611478 and -2.516611478.Subproblem 1
x + -3 = 2.516611478 Simplifying x + -3 = 2.516611478 Reorder the terms: -3 + x = 2.516611478 Solving -3 + x = 2.516611478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.516611478 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.516611478 + 3 x = 2.516611478 + 3 Combine like terms: 2.516611478 + 3 = 5.516611478 x = 5.516611478 Simplifying x = 5.516611478Subproblem 2
x + -3 = -2.516611478 Simplifying x + -3 = -2.516611478 Reorder the terms: -3 + x = -2.516611478 Solving -3 + x = -2.516611478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.516611478 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.516611478 + 3 x = -2.516611478 + 3 Combine like terms: -2.516611478 + 3 = 0.483388522 x = 0.483388522 Simplifying x = 0.483388522Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.516611478, 0.483388522}
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