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Simplifying 3x(x + 6) + 2(x + 12) = 0 Reorder the terms: 3x(6 + x) + 2(x + 12) = 0 (6 * 3x + x * 3x) + 2(x + 12) = 0 (18x + 3x2) + 2(x + 12) = 0 Reorder the terms: 18x + 3x2 + 2(12 + x) = 0 18x + 3x2 + (12 * 2 + x * 2) = 0 18x + 3x2 + (24 + 2x) = 0 Reorder the terms: 24 + 18x + 2x + 3x2 = 0 Combine like terms: 18x + 2x = 20x 24 + 20x + 3x2 = 0 Solving 24 + 20x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 6.666666667x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 6.666666667x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 6.666666667x + x2 = 0 + -8 6.666666667x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 6.666666667x + x2 = -8 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = -8 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = -8 + 11.11111112 Combine like terms: -8 + 11.11111112 = 3.11111112 11.11111112 + 6.666666667x + x2 = 3.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 3.11111112 Calculate the square root of the right side: 1.76383421 Break this problem into two subproblems by setting (x + 3.333333334) equal to 1.76383421 and -1.76383421.Subproblem 1
x + 3.333333334 = 1.76383421 Simplifying x + 3.333333334 = 1.76383421 Reorder the terms: 3.333333334 + x = 1.76383421 Solving 3.333333334 + x = 1.76383421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 1.76383421 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 1.76383421 + -3.333333334 x = 1.76383421 + -3.333333334 Combine like terms: 1.76383421 + -3.333333334 = -1.569499124 x = -1.569499124 Simplifying x = -1.569499124Subproblem 2
x + 3.333333334 = -1.76383421 Simplifying x + 3.333333334 = -1.76383421 Reorder the terms: 3.333333334 + x = -1.76383421 Solving 3.333333334 + x = -1.76383421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -1.76383421 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -1.76383421 + -3.333333334 x = -1.76383421 + -3.333333334 Combine like terms: -1.76383421 + -3.333333334 = -5.097167544 x = -5.097167544 Simplifying x = -5.097167544Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.569499124, -5.097167544}
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