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Simplifying (3x + 3)(x + 2) = 1 Reorder the terms: (3 + 3x)(x + 2) = 1 Reorder the terms: (3 + 3x)(2 + x) = 1 Multiply (3 + 3x) * (2 + x) (3(2 + x) + 3x * (2 + x)) = 1 ((2 * 3 + x * 3) + 3x * (2 + x)) = 1 ((6 + 3x) + 3x * (2 + x)) = 1 (6 + 3x + (2 * 3x + x * 3x)) = 1 (6 + 3x + (6x + 3x2)) = 1 Combine like terms: 3x + 6x = 9x (6 + 9x + 3x2) = 1 Solving 6 + 9x + 3x2 = 1 Solving for variable 'x'. Reorder the terms: 6 + -1 + 9x + 3x2 = 1 + -1 Combine like terms: 6 + -1 = 5 5 + 9x + 3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 5 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 3x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 3x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + -1.666666667 3x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 3x + x2 = -1.666666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.666666667 + 2.25 Combine like terms: -1.666666667 + 2.25 = 0.583333333 2.25 + 3x + x2 = 0.583333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.583333333 Calculate the square root of the right side: 0.763762616 Break this problem into two subproblems by setting (x + 1.5) equal to 0.763762616 and -0.763762616.Subproblem 1
x + 1.5 = 0.763762616 Simplifying x + 1.5 = 0.763762616 Reorder the terms: 1.5 + x = 0.763762616 Solving 1.5 + x = 0.763762616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.763762616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.763762616 + -1.5 x = 0.763762616 + -1.5 Combine like terms: 0.763762616 + -1.5 = -0.736237384 x = -0.736237384 Simplifying x = -0.736237384Subproblem 2
x + 1.5 = -0.763762616 Simplifying x + 1.5 = -0.763762616 Reorder the terms: 1.5 + x = -0.763762616 Solving 1.5 + x = -0.763762616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.763762616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.763762616 + -1.5 x = -0.763762616 + -1.5 Combine like terms: -0.763762616 + -1.5 = -2.263762616 x = -2.263762616 Simplifying x = -2.263762616Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.736237384, -2.263762616}
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