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Simplifying x(3x + 2) = 432 Reorder the terms: x(2 + 3x) = 432 (2 * x + 3x * x) = 432 (2x + 3x2) = 432 Solving 2x + 3x2 = 432 Solving for variable 'x'. Reorder the terms: -432 + 2x + 3x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -432 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -144 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 0.6666666667x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 0.6666666667x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 0.6666666667x + x2 = 0 + 144 0.6666666667x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 0.6666666667x + x2 = 144 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 144 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 144 + 0.1111111112 Combine like terms: 144 + 0.1111111112 = 144.1111111112 0.1111111112 + 0.6666666667x + x2 = 144.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 144.1111111112 Calculate the square root of the right side: 12.004628737 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 12.004628737 and -12.004628737.Subproblem 1
x + 0.3333333334 = 12.004628737 Simplifying x + 0.3333333334 = 12.004628737 Reorder the terms: 0.3333333334 + x = 12.004628737 Solving 0.3333333334 + x = 12.004628737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 12.004628737 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 12.004628737 + -0.3333333334 x = 12.004628737 + -0.3333333334 Combine like terms: 12.004628737 + -0.3333333334 = 11.6712954036 x = 11.6712954036 Simplifying x = 11.6712954036Subproblem 2
x + 0.3333333334 = -12.004628737 Simplifying x + 0.3333333334 = -12.004628737 Reorder the terms: 0.3333333334 + x = -12.004628737 Solving 0.3333333334 + x = -12.004628737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -12.004628737 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -12.004628737 + -0.3333333334 x = -12.004628737 + -0.3333333334 Combine like terms: -12.004628737 + -0.3333333334 = -12.3379620704 x = -12.3379620704 Simplifying x = -12.3379620704Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.6712954036, -12.3379620704}
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