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Simplifying 2x(x + 1) + 9 = (3x + 1)(x + -1) Reorder the terms: 2x(1 + x) + 9 = (3x + 1)(x + -1) (1 * 2x + x * 2x) + 9 = (3x + 1)(x + -1) (2x + 2x2) + 9 = (3x + 1)(x + -1) Reorder the terms: 9 + 2x + 2x2 = (3x + 1)(x + -1) Reorder the terms: 9 + 2x + 2x2 = (1 + 3x)(x + -1) Reorder the terms: 9 + 2x + 2x2 = (1 + 3x)(-1 + x) Multiply (1 + 3x) * (-1 + x) 9 + 2x + 2x2 = (1(-1 + x) + 3x * (-1 + x)) 9 + 2x + 2x2 = ((-1 * 1 + x * 1) + 3x * (-1 + x)) 9 + 2x + 2x2 = ((-1 + 1x) + 3x * (-1 + x)) 9 + 2x + 2x2 = (-1 + 1x + (-1 * 3x + x * 3x)) 9 + 2x + 2x2 = (-1 + 1x + (-3x + 3x2)) Combine like terms: 1x + -3x = -2x 9 + 2x + 2x2 = (-1 + -2x + 3x2) Solving 9 + 2x + 2x2 = -1 + -2x + 3x2 Solving for variable 'x'. Reorder the terms: 9 + 1 + 2x + 2x + 2x2 + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2 Combine like terms: 9 + 1 = 10 10 + 2x + 2x + 2x2 + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2 Combine like terms: 2x + 2x = 4x 10 + 4x + 2x2 + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 10 + 4x + -1x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2 Reorder the terms: 10 + 4x + -1x2 = -1 + 1 + -2x + 2x + 3x2 + -3x2 Combine like terms: -1 + 1 = 0 10 + 4x + -1x2 = 0 + -2x + 2x + 3x2 + -3x2 10 + 4x + -1x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 10 + 4x + -1x2 = 0 + 3x2 + -3x2 10 + 4x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 10 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -4x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -4x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4x + x2 = 0 + 10 -4x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4x + x2 = 10 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 = 10 + 4 Reorder the terms: 4 + -4x + x2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4x + x2 = 14 Factor a perfect square on the left side: (x + -2)(x + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -2 = 3.741657387 Simplifying x + -2 = 3.741657387 Reorder the terms: -2 + x = 3.741657387 Solving -2 + x = 3.741657387 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 = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.741657387 + 2 x = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 x = 5.741657387 Simplifying x = 5.741657387Subproblem 2
x + -2 = -3.741657387 Simplifying x + -2 = -3.741657387 Reorder the terms: -2 + x = -3.741657387 Solving -2 + x = -3.741657387 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 = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.741657387 + 2 x = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 x = -1.741657387 Simplifying x = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.741657387, -1.741657387}
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