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Simplifying (2x + -1)(x + 1) = 3 Reorder the terms: (-1 + 2x)(x + 1) = 3 Reorder the terms: (-1 + 2x)(1 + x) = 3 Multiply (-1 + 2x) * (1 + x) (-1(1 + x) + 2x * (1 + x)) = 3 ((1 * -1 + x * -1) + 2x * (1 + x)) = 3 ((-1 + -1x) + 2x * (1 + x)) = 3 (-1 + -1x + (1 * 2x + x * 2x)) = 3 (-1 + -1x + (2x + 2x2)) = 3 Combine like terms: -1x + 2x = 1x (-1 + 1x + 2x2) = 3 Solving -1 + 1x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -1 + -3 + 1x + 2x2 = 3 + -3 Combine like terms: -1 + -3 = -4 -4 + 1x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -4 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 0.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5x + x2 = 0 + 2 0.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5x + x2 = 2 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 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + 0.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + 0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + 0.25 = 1.436140662 Simplifying x + 0.25 = 1.436140662 Reorder the terms: 0.25 + x = 1.436140662 Solving 0.25 + x = 1.436140662 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 = 1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.436140662 + -0.25 x = 1.436140662 + -0.25 Combine like terms: 1.436140662 + -0.25 = 1.186140662 x = 1.186140662 Simplifying x = 1.186140662Subproblem 2
x + 0.25 = -1.436140662 Simplifying x + 0.25 = -1.436140662 Reorder the terms: 0.25 + x = -1.436140662 Solving 0.25 + x = -1.436140662 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 = -1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.436140662 + -0.25 x = -1.436140662 + -0.25 Combine like terms: -1.436140662 + -0.25 = -1.686140662 x = -1.686140662 Simplifying x = -1.686140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.186140662, -1.686140662}
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