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Simplifying 2(x + 12) = 3x(x + 3) Reorder the terms: 2(12 + x) = 3x(x + 3) (12 * 2 + x * 2) = 3x(x + 3) (24 + 2x) = 3x(x + 3) Reorder the terms: 24 + 2x = 3x(3 + x) 24 + 2x = (3 * 3x + x * 3x) 24 + 2x = (9x + 3x2) Solving 24 + 2x = 9x + 3x2 Solving for variable 'x'. Combine like terms: 2x + -9x = -7x 24 + -7x + -3x2 = 9x + 3x2 + -9x + -3x2 Reorder the terms: 24 + -7x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 24 + -7x + -3x2 = 0 + 3x2 + -3x2 24 + -7x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 24 + -7x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -8 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 2.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.333333333x + x2 = 0 + 8 2.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.333333333x + x2 = 8 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 8 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 8 + 1.361111112 Combine like terms: 8 + 1.361111112 = 9.361111112 1.361111112 + 2.333333333x + x2 = 9.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 9.361111112 Calculate the square root of the right side: 3.059593292 Break this problem into two subproblems by setting (x + 1.166666667) equal to 3.059593292 and -3.059593292.Subproblem 1
x + 1.166666667 = 3.059593292 Simplifying x + 1.166666667 = 3.059593292 Reorder the terms: 1.166666667 + x = 3.059593292 Solving 1.166666667 + x = 3.059593292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 3.059593292 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 3.059593292 + -1.166666667 x = 3.059593292 + -1.166666667 Combine like terms: 3.059593292 + -1.166666667 = 1.892926625 x = 1.892926625 Simplifying x = 1.892926625Subproblem 2
x + 1.166666667 = -3.059593292 Simplifying x + 1.166666667 = -3.059593292 Reorder the terms: 1.166666667 + x = -3.059593292 Solving 1.166666667 + x = -3.059593292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -3.059593292 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -3.059593292 + -1.166666667 x = -3.059593292 + -1.166666667 Combine like terms: -3.059593292 + -1.166666667 = -4.226259959 x = -4.226259959 Simplifying x = -4.226259959Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.892926625, -4.226259959}
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