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Simplifying 3x(x + 4) = 2 Reorder the terms: 3x(4 + x) = 2 (4 * 3x + x * 3x) = 2 (12x + 3x2) = 2 Solving 12x + 3x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 12x + 3x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 4x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 4x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 4x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + 0.6666666667 4x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 4x + x2 = 0.6666666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 0.6666666667 + 4 Reorder the terms: 4 + 4x + x2 = 0.6666666667 + 4 Combine like terms: 0.6666666667 + 4 = 4.6666666667 4 + 4x + x2 = 4.6666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.6666666667 Calculate the square root of the right side: 2.160246899 Break this problem into two subproblems by setting (x + 2) equal to 2.160246899 and -2.160246899.Subproblem 1
x + 2 = 2.160246899 Simplifying x + 2 = 2.160246899 Reorder the terms: 2 + x = 2.160246899 Solving 2 + x = 2.160246899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.160246899 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.160246899 + -2 x = 2.160246899 + -2 Combine like terms: 2.160246899 + -2 = 0.160246899 x = 0.160246899 Simplifying x = 0.160246899Subproblem 2
x + 2 = -2.160246899 Simplifying x + 2 = -2.160246899 Reorder the terms: 2 + x = -2.160246899 Solving 2 + x = -2.160246899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.160246899 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.160246899 + -2 x = -2.160246899 + -2 Combine like terms: -2.160246899 + -2 = -4.160246899 x = -4.160246899 Simplifying x = -4.160246899Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.160246899, -4.160246899}
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