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Simplifying 3x(3x + 8) = 164 Reorder the terms: 3x(8 + 3x) = 164 (8 * 3x + 3x * 3x) = 164 (24x + 9x2) = 164 Solving 24x + 9x2 = 164 Solving for variable 'x'. Reorder the terms: -164 + 24x + 9x2 = 164 + -164 Combine like terms: 164 + -164 = 0 -164 + 24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -18.22222222 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '18.22222222' to each side of the equation. -18.22222222 + 2.666666667x + 18.22222222 + x2 = 0 + 18.22222222 Reorder the terms: -18.22222222 + 18.22222222 + 2.666666667x + x2 = 0 + 18.22222222 Combine like terms: -18.22222222 + 18.22222222 = 0.00000000 0.00000000 + 2.666666667x + x2 = 0 + 18.22222222 2.666666667x + x2 = 0 + 18.22222222 Combine like terms: 0 + 18.22222222 = 18.22222222 2.666666667x + x2 = 18.22222222 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 = 18.22222222 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 18.22222222 + 1.777777780 Combine like terms: 18.22222222 + 1.777777780 = 20 1.777777780 + 2.666666667x + x2 = 20 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 1.333333334) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 1.333333334 = 4.472135955 Simplifying x + 1.333333334 = 4.472135955 Reorder the terms: 1.333333334 + x = 4.472135955 Solving 1.333333334 + x = 4.472135955 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 = 4.472135955 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 4.472135955 + -1.333333334 x = 4.472135955 + -1.333333334 Combine like terms: 4.472135955 + -1.333333334 = 3.138802621 x = 3.138802621 Simplifying x = 3.138802621Subproblem 2
x + 1.333333334 = -4.472135955 Simplifying x + 1.333333334 = -4.472135955 Reorder the terms: 1.333333334 + x = -4.472135955 Solving 1.333333334 + x = -4.472135955 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 = -4.472135955 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -4.472135955 + -1.333333334 x = -4.472135955 + -1.333333334 Combine like terms: -4.472135955 + -1.333333334 = -5.805469289 x = -5.805469289 Simplifying x = -5.805469289Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.138802621, -5.805469289}
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