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Simplifying (3x + -1)(x + -3) + 4x + -19 = 0 Reorder the terms: (-1 + 3x)(x + -3) + 4x + -19 = 0 Reorder the terms: (-1 + 3x)(-3 + x) + 4x + -19 = 0 Multiply (-1 + 3x) * (-3 + x) (-1(-3 + x) + 3x * (-3 + x)) + 4x + -19 = 0 ((-3 * -1 + x * -1) + 3x * (-3 + x)) + 4x + -19 = 0 ((3 + -1x) + 3x * (-3 + x)) + 4x + -19 = 0 (3 + -1x + (-3 * 3x + x * 3x)) + 4x + -19 = 0 (3 + -1x + (-9x + 3x2)) + 4x + -19 = 0 Combine like terms: -1x + -9x = -10x (3 + -10x + 3x2) + 4x + -19 = 0 Reorder the terms: 3 + -19 + -10x + 4x + 3x2 = 0 Combine like terms: 3 + -19 = -16 -16 + -10x + 4x + 3x2 = 0 Combine like terms: -10x + 4x = -6x -16 + -6x + 3x2 = 0 Solving -16 + -6x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -2x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -2x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 5.333333333 -2x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -2x + x2 = 5.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 5.333333333 + 1 Combine like terms: 5.333333333 + 1 = 6.333333333 1 + -2x + x2 = 6.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (x + -1) equal to 2.516611478 and -2.516611478.Subproblem 1
x + -1 = 2.516611478 Simplifying x + -1 = 2.516611478 Reorder the terms: -1 + x = 2.516611478 Solving -1 + x = 2.516611478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.516611478 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.516611478 + 1 x = 2.516611478 + 1 Combine like terms: 2.516611478 + 1 = 3.516611478 x = 3.516611478 Simplifying x = 3.516611478Subproblem 2
x + -1 = -2.516611478 Simplifying x + -1 = -2.516611478 Reorder the terms: -1 + x = -2.516611478 Solving -1 + x = -2.516611478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.516611478 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.516611478 + 1 x = -2.516611478 + 1 Combine like terms: -2.516611478 + 1 = -1.516611478 x = -1.516611478 Simplifying x = -1.516611478Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.516611478, -1.516611478}
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