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Simplifying (2x + 5)(x + -1) = 2x Reorder the terms: (5 + 2x)(x + -1) = 2x Reorder the terms: (5 + 2x)(-1 + x) = 2x Multiply (5 + 2x) * (-1 + x) (5(-1 + x) + 2x * (-1 + x)) = 2x ((-1 * 5 + x * 5) + 2x * (-1 + x)) = 2x ((-5 + 5x) + 2x * (-1 + x)) = 2x (-5 + 5x + (-1 * 2x + x * 2x)) = 2x (-5 + 5x + (-2x + 2x2)) = 2x Combine like terms: 5x + -2x = 3x (-5 + 3x + 2x2) = 2x Solving -5 + 3x + 2x2 = 2x Solving for variable 'x'. Reorder the terms: -5 + 3x + -2x + 2x2 = 2x + -2x Combine like terms: 3x + -2x = 1x -5 + 1x + 2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -5 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.5x + x2 = 0 + 2.5 0.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.5x + x2 = 2.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + 0.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + 0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + 0.25 = 1.600781059 Simplifying x + 0.25 = 1.600781059 Reorder the terms: 0.25 + x = 1.600781059 Solving 0.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.600781059 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.600781059 + -0.25 x = 1.600781059 + -0.25 Combine like terms: 1.600781059 + -0.25 = 1.350781059 x = 1.350781059 Simplifying x = 1.350781059Subproblem 2
x + 0.25 = -1.600781059 Simplifying x + 0.25 = -1.600781059 Reorder the terms: 0.25 + x = -1.600781059 Solving 0.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.600781059 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.600781059 + -0.25 x = -1.600781059 + -0.25 Combine like terms: -1.600781059 + -0.25 = -1.850781059 x = -1.850781059 Simplifying x = -1.850781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.350781059, -1.850781059}
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