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Simplifying (x + -3)(2x + 3) = 2x + -5 Reorder the terms: (-3 + x)(2x + 3) = 2x + -5 Reorder the terms: (-3 + x)(3 + 2x) = 2x + -5 Multiply (-3 + x) * (3 + 2x) (-3(3 + 2x) + x(3 + 2x)) = 2x + -5 ((3 * -3 + 2x * -3) + x(3 + 2x)) = 2x + -5 ((-9 + -6x) + x(3 + 2x)) = 2x + -5 (-9 + -6x + (3 * x + 2x * x)) = 2x + -5 (-9 + -6x + (3x + 2x2)) = 2x + -5 Combine like terms: -6x + 3x = -3x (-9 + -3x + 2x2) = 2x + -5 Reorder the terms: -9 + -3x + 2x2 = -5 + 2x Solving -9 + -3x + 2x2 = -5 + 2x Solving for variable 'x'. Reorder the terms: -9 + 5 + -3x + -2x + 2x2 = -5 + 2x + 5 + -2x Combine like terms: -9 + 5 = -4 -4 + -3x + -2x + 2x2 = -5 + 2x + 5 + -2x Combine like terms: -3x + -2x = -5x -4 + -5x + 2x2 = -5 + 2x + 5 + -2x Reorder the terms: -4 + -5x + 2x2 = -5 + 5 + 2x + -2x Combine like terms: -5 + 5 = 0 -4 + -5x + 2x2 = 0 + 2x + -2x -4 + -5x + 2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -4 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -2.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.5x + x2 = 0 + 2 -2.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.5x + x2 = 2 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 2 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + -2.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + -1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + -1.25 = 1.887458609 Simplifying x + -1.25 = 1.887458609 Reorder the terms: -1.25 + x = 1.887458609 Solving -1.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.887458609 + 1.25 x = 1.887458609 + 1.25 Combine like terms: 1.887458609 + 1.25 = 3.137458609 x = 3.137458609 Simplifying x = 3.137458609Subproblem 2
x + -1.25 = -1.887458609 Simplifying x + -1.25 = -1.887458609 Reorder the terms: -1.25 + x = -1.887458609 Solving -1.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.887458609 + 1.25 x = -1.887458609 + 1.25 Combine like terms: -1.887458609 + 1.25 = -0.637458609 x = -0.637458609 Simplifying x = -0.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.137458609, -0.637458609}
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