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Simplifying 3x(x + 4) = x + 18 Reorder the terms: 3x(4 + x) = x + 18 (4 * 3x + x * 3x) = x + 18 (12x + 3x2) = x + 18 Reorder the terms: 12x + 3x2 = 18 + x Solving 12x + 3x2 = 18 + x Solving for variable 'x'. Reorder the terms: -18 + 12x + -1x + 3x2 = 18 + x + -18 + -1x Combine like terms: 12x + -1x = 11x -18 + 11x + 3x2 = 18 + x + -18 + -1x Reorder the terms: -18 + 11x + 3x2 = 18 + -18 + x + -1x Combine like terms: 18 + -18 = 0 -18 + 11x + 3x2 = 0 + x + -1x -18 + 11x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -18 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 3.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3.666666667x + x2 = 0 + 6 3.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 3.666666667x + x2 = 6 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 = 6 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = 6 + 3.361111114 Combine like terms: 6 + 3.361111114 = 9.361111114 3.361111114 + 3.666666667x + x2 = 9.361111114 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 9.361111114 Calculate the square root of the right side: 3.059593292 Break this problem into two subproblems by setting (x + 1.833333334) equal to 3.059593292 and -3.059593292.Subproblem 1
x + 1.833333334 = 3.059593292 Simplifying x + 1.833333334 = 3.059593292 Reorder the terms: 1.833333334 + x = 3.059593292 Solving 1.833333334 + x = 3.059593292 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 = 3.059593292 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 3.059593292 + -1.833333334 x = 3.059593292 + -1.833333334 Combine like terms: 3.059593292 + -1.833333334 = 1.226259958 x = 1.226259958 Simplifying x = 1.226259958Subproblem 2
x + 1.833333334 = -3.059593292 Simplifying x + 1.833333334 = -3.059593292 Reorder the terms: 1.833333334 + x = -3.059593292 Solving 1.833333334 + x = -3.059593292 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 = -3.059593292 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -3.059593292 + -1.833333334 x = -3.059593292 + -1.833333334 Combine like terms: -3.059593292 + -1.833333334 = -4.892926626 x = -4.892926626 Simplifying x = -4.892926626Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.226259958, -4.892926626}
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