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Simplifying (1 + -4)(3x + -7) = (x + -2)(3x + 7) + x Combine like terms: 1 + -4 = -3 (-3)(3x + -7) = (x + -2)(3x + 7) + x Reorder the terms: -3(-7 + 3x) = (x + -2)(3x + 7) + x (-7 * -3 + 3x * -3) = (x + -2)(3x + 7) + x (21 + -9x) = (x + -2)(3x + 7) + x Reorder the terms: 21 + -9x = (-2 + x)(3x + 7) + x Reorder the terms: 21 + -9x = (-2 + x)(7 + 3x) + x Multiply (-2 + x) * (7 + 3x) 21 + -9x = (-2(7 + 3x) + x(7 + 3x)) + x 21 + -9x = ((7 * -2 + 3x * -2) + x(7 + 3x)) + x 21 + -9x = ((-14 + -6x) + x(7 + 3x)) + x 21 + -9x = (-14 + -6x + (7 * x + 3x * x)) + x 21 + -9x = (-14 + -6x + (7x + 3x2)) + x Combine like terms: -6x + 7x = 1x 21 + -9x = (-14 + 1x + 3x2) + x Reorder the terms: 21 + -9x = -14 + 1x + x + 3x2 Combine like terms: 1x + x = 2x 21 + -9x = -14 + 2x + 3x2 Solving 21 + -9x = -14 + 2x + 3x2 Solving for variable 'x'. Reorder the terms: 21 + 14 + -9x + -2x + -3x2 = -14 + 2x + 3x2 + 14 + -2x + -3x2 Combine like terms: 21 + 14 = 35 35 + -9x + -2x + -3x2 = -14 + 2x + 3x2 + 14 + -2x + -3x2 Combine like terms: -9x + -2x = -11x 35 + -11x + -3x2 = -14 + 2x + 3x2 + 14 + -2x + -3x2 Reorder the terms: 35 + -11x + -3x2 = -14 + 14 + 2x + -2x + 3x2 + -3x2 Combine like terms: -14 + 14 = 0 35 + -11x + -3x2 = 0 + 2x + -2x + 3x2 + -3x2 35 + -11x + -3x2 = 2x + -2x + 3x2 + -3x2 Combine like terms: 2x + -2x = 0 35 + -11x + -3x2 = 0 + 3x2 + -3x2 35 + -11x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 35 + -11x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -11.66666667 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + 3.666666667x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + 3.666666667x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + 3.666666667x + x2 = 0 + 11.66666667 3.666666667x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 3.666666667x + x2 = 11.66666667 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = 11.66666667 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 11.66666667 + 3.361111114 Combine like terms: 11.66666667 + 3.361111114 = 15.027777784 3.361111114 + 3.666666667x + x2 = 15.027777784 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 15.027777784 Calculate the square root of the right side: 3.876567784 Break this problem into two subproblems by setting (x + 1.833333334) equal to 3.876567784 and -3.876567784.Subproblem 1
x + 1.833333334 = 3.876567784 Simplifying x + 1.833333334 = 3.876567784 Reorder the terms: 1.833333334 + x = 3.876567784 Solving 1.833333334 + x = 3.876567784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 3.876567784 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 3.876567784 + -1.833333334 x = 3.876567784 + -1.833333334 Combine like terms: 3.876567784 + -1.833333334 = 2.04323445 x = 2.04323445 Simplifying x = 2.04323445Subproblem 2
x + 1.833333334 = -3.876567784 Simplifying x + 1.833333334 = -3.876567784 Reorder the terms: 1.833333334 + x = -3.876567784 Solving 1.833333334 + x = -3.876567784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -3.876567784 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -3.876567784 + -1.833333334 x = -3.876567784 + -1.833333334 Combine like terms: -3.876567784 + -1.833333334 = -5.709901118 x = -5.709901118 Simplifying x = -5.709901118Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.04323445, -5.709901118}
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