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Simplifying (3x + 1)(x + -1) + -3(x + 2) = 9 Reorder the terms: (1 + 3x)(x + -1) + -3(x + 2) = 9 Reorder the terms: (1 + 3x)(-1 + x) + -3(x + 2) = 9 Multiply (1 + 3x) * (-1 + x) (1(-1 + x) + 3x * (-1 + x)) + -3(x + 2) = 9 ((-1 * 1 + x * 1) + 3x * (-1 + x)) + -3(x + 2) = 9 ((-1 + 1x) + 3x * (-1 + x)) + -3(x + 2) = 9 (-1 + 1x + (-1 * 3x + x * 3x)) + -3(x + 2) = 9 (-1 + 1x + (-3x + 3x2)) + -3(x + 2) = 9 Combine like terms: 1x + -3x = -2x (-1 + -2x + 3x2) + -3(x + 2) = 9 Reorder the terms: -1 + -2x + 3x2 + -3(2 + x) = 9 -1 + -2x + 3x2 + (2 * -3 + x * -3) = 9 -1 + -2x + 3x2 + (-6 + -3x) = 9 Reorder the terms: -1 + -6 + -2x + -3x + 3x2 = 9 Combine like terms: -1 + -6 = -7 -7 + -2x + -3x + 3x2 = 9 Combine like terms: -2x + -3x = -5x -7 + -5x + 3x2 = 9 Solving -7 + -5x + 3x2 = 9 Solving for variable 'x'. Reorder the terms: -7 + -9 + -5x + 3x2 = 9 + -9 Combine like terms: -7 + -9 = -16 -16 + -5x + 3x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -16 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -1.666666667x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -1.666666667x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 5.333333333 -1.666666667x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -1.666666667x + x2 = 5.333333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 5.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 5.333333333 + 0.6944444447 Combine like terms: 5.333333333 + 0.6944444447 = 6.0277777777 0.6944444447 + -1.666666667x + x2 = 6.0277777777 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 6.0277777777 Calculate the square root of the right side: 2.45515331 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.45515331 and -2.45515331.Subproblem 1
x + -0.8333333335 = 2.45515331 Simplifying x + -0.8333333335 = 2.45515331 Reorder the terms: -0.8333333335 + x = 2.45515331 Solving -0.8333333335 + x = 2.45515331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 2.45515331 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.45515331 + 0.8333333335 x = 2.45515331 + 0.8333333335 Combine like terms: 2.45515331 + 0.8333333335 = 3.2884866435 x = 3.2884866435 Simplifying x = 3.2884866435Subproblem 2
x + -0.8333333335 = -2.45515331 Simplifying x + -0.8333333335 = -2.45515331 Reorder the terms: -0.8333333335 + x = -2.45515331 Solving -0.8333333335 + x = -2.45515331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -2.45515331 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.45515331 + 0.8333333335 x = -2.45515331 + 0.8333333335 Combine like terms: -2.45515331 + 0.8333333335 = -1.6218199765 x = -1.6218199765 Simplifying x = -1.6218199765Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2884866435, -1.6218199765}
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