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Simplifying 3x + -1(x + -2) = (2x + -1)(-3x + 9) Reorder the terms: 3x + -1(-2 + x) = (2x + -1)(-3x + 9) 3x + (-2 * -1 + x * -1) = (2x + -1)(-3x + 9) 3x + (2 + -1x) = (2x + -1)(-3x + 9) Reorder the terms: 2 + 3x + -1x = (2x + -1)(-3x + 9) Combine like terms: 3x + -1x = 2x 2 + 2x = (2x + -1)(-3x + 9) Reorder the terms: 2 + 2x = (-1 + 2x)(-3x + 9) Reorder the terms: 2 + 2x = (-1 + 2x)(9 + -3x) Multiply (-1 + 2x) * (9 + -3x) 2 + 2x = (-1(9 + -3x) + 2x * (9 + -3x)) 2 + 2x = ((9 * -1 + -3x * -1) + 2x * (9 + -3x)) 2 + 2x = ((-9 + 3x) + 2x * (9 + -3x)) 2 + 2x = (-9 + 3x + (9 * 2x + -3x * 2x)) 2 + 2x = (-9 + 3x + (18x + -6x2)) Combine like terms: 3x + 18x = 21x 2 + 2x = (-9 + 21x + -6x2) Solving 2 + 2x = -9 + 21x + -6x2 Solving for variable 'x'. Reorder the terms: 2 + 9 + 2x + -21x + 6x2 = -9 + 21x + -6x2 + 9 + -21x + 6x2 Combine like terms: 2 + 9 = 11 11 + 2x + -21x + 6x2 = -9 + 21x + -6x2 + 9 + -21x + 6x2 Combine like terms: 2x + -21x = -19x 11 + -19x + 6x2 = -9 + 21x + -6x2 + 9 + -21x + 6x2 Reorder the terms: 11 + -19x + 6x2 = -9 + 9 + 21x + -21x + -6x2 + 6x2 Combine like terms: -9 + 9 = 0 11 + -19x + 6x2 = 0 + 21x + -21x + -6x2 + 6x2 11 + -19x + 6x2 = 21x + -21x + -6x2 + 6x2 Combine like terms: 21x + -21x = 0 11 + -19x + 6x2 = 0 + -6x2 + 6x2 11 + -19x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 11 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -3.166666667x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -3.166666667x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + -1.833333333 -3.166666667x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -3.166666667x + x2 = -1.833333333 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = -1.833333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -1.833333333 + 2.506944447 Combine like terms: -1.833333333 + 2.506944447 = 0.673611114 2.506944447 + -3.166666667x + x2 = 0.673611114 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 0.673611114 Calculate the square root of the right side: 0.820738152 Break this problem into two subproblems by setting (x + -1.583333334) equal to 0.820738152 and -0.820738152.Subproblem 1
x + -1.583333334 = 0.820738152 Simplifying x + -1.583333334 = 0.820738152 Reorder the terms: -1.583333334 + x = 0.820738152 Solving -1.583333334 + x = 0.820738152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 0.820738152 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 0.820738152 + 1.583333334 x = 0.820738152 + 1.583333334 Combine like terms: 0.820738152 + 1.583333334 = 2.404071486 x = 2.404071486 Simplifying x = 2.404071486Subproblem 2
x + -1.583333334 = -0.820738152 Simplifying x + -1.583333334 = -0.820738152 Reorder the terms: -1.583333334 + x = -0.820738152 Solving -1.583333334 + x = -0.820738152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -0.820738152 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -0.820738152 + 1.583333334 x = -0.820738152 + 1.583333334 Combine like terms: -0.820738152 + 1.583333334 = 0.762595182 x = 0.762595182 Simplifying x = 0.762595182Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.404071486, 0.762595182}
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