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Simplifying 2x(x + 2) = (3x + -1)(x + 3) Reorder the terms: 2x(2 + x) = (3x + -1)(x + 3) (2 * 2x + x * 2x) = (3x + -1)(x + 3) (4x + 2x2) = (3x + -1)(x + 3) Reorder the terms: 4x + 2x2 = (-1 + 3x)(x + 3) Reorder the terms: 4x + 2x2 = (-1 + 3x)(3 + x) Multiply (-1 + 3x) * (3 + x) 4x + 2x2 = (-1(3 + x) + 3x * (3 + x)) 4x + 2x2 = ((3 * -1 + x * -1) + 3x * (3 + x)) 4x + 2x2 = ((-3 + -1x) + 3x * (3 + x)) 4x + 2x2 = (-3 + -1x + (3 * 3x + x * 3x)) 4x + 2x2 = (-3 + -1x + (9x + 3x2)) Combine like terms: -1x + 9x = 8x 4x + 2x2 = (-3 + 8x + 3x2) Solving 4x + 2x2 = -3 + 8x + 3x2 Solving for variable 'x'. Reorder the terms: 3 + 4x + -8x + 2x2 + -3x2 = -3 + 8x + 3x2 + 3 + -8x + -3x2 Combine like terms: 4x + -8x = -4x 3 + -4x + 2x2 + -3x2 = -3 + 8x + 3x2 + 3 + -8x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 3 + -4x + -1x2 = -3 + 8x + 3x2 + 3 + -8x + -3x2 Reorder the terms: 3 + -4x + -1x2 = -3 + 3 + 8x + -8x + 3x2 + -3x2 Combine like terms: -3 + 3 = 0 3 + -4x + -1x2 = 0 + 8x + -8x + 3x2 + -3x2 3 + -4x + -1x2 = 8x + -8x + 3x2 + -3x2 Combine like terms: 8x + -8x = 0 3 + -4x + -1x2 = 0 + 3x2 + -3x2 3 + -4x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x + x2 = 0 + 3 4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x + x2 = 3 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 = 3 + 4 Reorder the terms: 4 + 4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4x + x2 = 7 Factor a perfect square on the left side: (x + 2)(x + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 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 = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311Subproblem 2
x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 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 = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}
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