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Simplifying (x + 4)(3x + -4) = 448 Reorder the terms: (4 + x)(3x + -4) = 448 Reorder the terms: (4 + x)(-4 + 3x) = 448 Multiply (4 + x) * (-4 + 3x) (4(-4 + 3x) + x(-4 + 3x)) = 448 ((-4 * 4 + 3x * 4) + x(-4 + 3x)) = 448 ((-16 + 12x) + x(-4 + 3x)) = 448 (-16 + 12x + (-4 * x + 3x * x)) = 448 (-16 + 12x + (-4x + 3x2)) = 448 Combine like terms: 12x + -4x = 8x (-16 + 8x + 3x2) = 448 Solving -16 + 8x + 3x2 = 448 Solving for variable 'x'. Reorder the terms: -16 + -448 + 8x + 3x2 = 448 + -448 Combine like terms: -16 + -448 = -464 -464 + 8x + 3x2 = 448 + -448 Combine like terms: 448 + -448 = 0 -464 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -154.6666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '154.6666667' to each side of the equation. -154.6666667 + 2.666666667x + 154.6666667 + x2 = 0 + 154.6666667 Reorder the terms: -154.6666667 + 154.6666667 + 2.666666667x + x2 = 0 + 154.6666667 Combine like terms: -154.6666667 + 154.6666667 = 0.0000000 0.0000000 + 2.666666667x + x2 = 0 + 154.6666667 2.666666667x + x2 = 0 + 154.6666667 Combine like terms: 0 + 154.6666667 = 154.6666667 2.666666667x + x2 = 154.6666667 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 154.6666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 154.6666667 + 1.777777780 Combine like terms: 154.6666667 + 1.777777780 = 156.44444448 1.777777780 + 2.666666667x + x2 = 156.44444448 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 156.44444448 Calculate the square root of the right side: 12.507775361 Break this problem into two subproblems by setting (x + 1.333333334) equal to 12.507775361 and -12.507775361.Subproblem 1
x + 1.333333334 = 12.507775361 Simplifying x + 1.333333334 = 12.507775361 Reorder the terms: 1.333333334 + x = 12.507775361 Solving 1.333333334 + x = 12.507775361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 12.507775361 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 12.507775361 + -1.333333334 x = 12.507775361 + -1.333333334 Combine like terms: 12.507775361 + -1.333333334 = 11.174442027 x = 11.174442027 Simplifying x = 11.174442027Subproblem 2
x + 1.333333334 = -12.507775361 Simplifying x + 1.333333334 = -12.507775361 Reorder the terms: 1.333333334 + x = -12.507775361 Solving 1.333333334 + x = -12.507775361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -12.507775361 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -12.507775361 + -1.333333334 x = -12.507775361 + -1.333333334 Combine like terms: -12.507775361 + -1.333333334 = -13.841108695 x = -13.841108695 Simplifying x = -13.841108695Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.174442027, -13.841108695}
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