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Simplifying (2x + -1)(x + -2) = 3 Reorder the terms: (-1 + 2x)(x + -2) = 3 Reorder the terms: (-1 + 2x)(-2 + x) = 3 Multiply (-1 + 2x) * (-2 + x) (-1(-2 + x) + 2x * (-2 + x)) = 3 ((-2 * -1 + x * -1) + 2x * (-2 + x)) = 3 ((2 + -1x) + 2x * (-2 + x)) = 3 (2 + -1x + (-2 * 2x + x * 2x)) = 3 (2 + -1x + (-4x + 2x2)) = 3 Combine like terms: -1x + -4x = -5x (2 + -5x + 2x2) = 3 Solving 2 + -5x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: 2 + -3 + -5x + 2x2 = 3 + -3 Combine like terms: 2 + -3 = -1 -1 + -5x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -1 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.5x + x2 = 0 + 0.5 -2.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.5x + x2 = 0.5 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 = 0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + -2.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + -1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + -1.25 = 1.436140662 Simplifying x + -1.25 = 1.436140662 Reorder the terms: -1.25 + x = 1.436140662 Solving -1.25 + x = 1.436140662 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 = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.436140662 + 1.25 x = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 x = 2.686140662 Simplifying x = 2.686140662Subproblem 2
x + -1.25 = -1.436140662 Simplifying x + -1.25 = -1.436140662 Reorder the terms: -1.25 + x = -1.436140662 Solving -1.25 + x = -1.436140662 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 = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.436140662 + 1.25 x = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 x = -0.186140662 Simplifying x = -0.186140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.686140662, -0.186140662}
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