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Simplifying (2x + -1)(x + 1) = 45 Reorder the terms: (-1 + 2x)(x + 1) = 45 Reorder the terms: (-1 + 2x)(1 + x) = 45 Multiply (-1 + 2x) * (1 + x) (-1(1 + x) + 2x * (1 + x)) = 45 ((1 * -1 + x * -1) + 2x * (1 + x)) = 45 ((-1 + -1x) + 2x * (1 + x)) = 45 (-1 + -1x + (1 * 2x + x * 2x)) = 45 (-1 + -1x + (2x + 2x2)) = 45 Combine like terms: -1x + 2x = 1x (-1 + 1x + 2x2) = 45 Solving -1 + 1x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -1 + -45 + 1x + 2x2 = 45 + -45 Combine like terms: -1 + -45 = -46 -46 + 1x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -46 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23 + 0.5x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 0.5x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 0.5x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 0.5x + x2 = 0 + 23 0.5x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 0.5x + x2 = 23 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 = 23 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 23 + 0.0625 Combine like terms: 23 + 0.0625 = 23.0625 0.0625 + 0.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + 0.25) equal to 4.802343178 and -4.802343178.Subproblem 1
x + 0.25 = 4.802343178 Simplifying x + 0.25 = 4.802343178 Reorder the terms: 0.25 + x = 4.802343178 Solving 0.25 + x = 4.802343178 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 = 4.802343178 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.802343178 + -0.25 x = 4.802343178 + -0.25 Combine like terms: 4.802343178 + -0.25 = 4.552343178 x = 4.552343178 Simplifying x = 4.552343178Subproblem 2
x + 0.25 = -4.802343178 Simplifying x + 0.25 = -4.802343178 Reorder the terms: 0.25 + x = -4.802343178 Solving 0.25 + x = -4.802343178 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 = -4.802343178 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.802343178 + -0.25 x = -4.802343178 + -0.25 Combine like terms: -4.802343178 + -0.25 = -5.052343178 x = -5.052343178 Simplifying x = -5.052343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.552343178, -5.052343178}
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