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Simplifying (x + -3)(2x + 3) = 8 + -5x Reorder the terms: (-3 + x)(2x + 3) = 8 + -5x Reorder the terms: (-3 + x)(3 + 2x) = 8 + -5x Multiply (-3 + x) * (3 + 2x) (-3(3 + 2x) + x(3 + 2x)) = 8 + -5x ((3 * -3 + 2x * -3) + x(3 + 2x)) = 8 + -5x ((-9 + -6x) + x(3 + 2x)) = 8 + -5x (-9 + -6x + (3 * x + 2x * x)) = 8 + -5x (-9 + -6x + (3x + 2x2)) = 8 + -5x Combine like terms: -6x + 3x = -3x (-9 + -3x + 2x2) = 8 + -5x Solving -9 + -3x + 2x2 = 8 + -5x Solving for variable 'x'. Reorder the terms: -9 + -8 + -3x + 5x + 2x2 = 8 + -5x + -8 + 5x Combine like terms: -9 + -8 = -17 -17 + -3x + 5x + 2x2 = 8 + -5x + -8 + 5x Combine like terms: -3x + 5x = 2x -17 + 2x + 2x2 = 8 + -5x + -8 + 5x Reorder the terms: -17 + 2x + 2x2 = 8 + -8 + -5x + 5x Combine like terms: 8 + -8 = 0 -17 + 2x + 2x2 = 0 + -5x + 5x -17 + 2x + 2x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -17 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x + x2 = 0 + 8.5 x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 x + x2 = 8.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 8.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 8.5 + 0.25 Combine like terms: 8.5 + 0.25 = 8.75 1.25 + x2 = 8.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + 0.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + 0.5 = 2.958039892 Simplifying x + 0.5 = 2.958039892 Reorder the terms: 0.5 + x = 2.958039892 Solving 0.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.958039892 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.958039892 + -0.5 x = 2.958039892 + -0.5 Combine like terms: 2.958039892 + -0.5 = 2.458039892 x = 2.458039892 Simplifying x = 2.458039892Subproblem 2
x + 0.5 = -2.958039892 Simplifying x + 0.5 = -2.958039892 Reorder the terms: 0.5 + x = -2.958039892 Solving 0.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.958039892 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.958039892 + -0.5 x = -2.958039892 + -0.5 Combine like terms: -2.958039892 + -0.5 = -3.458039892 x = -3.458039892 Simplifying x = -3.458039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.458039892, -3.458039892}
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