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Simplifying (2x + 1)(x + -3) = 3 Reorder the terms: (1 + 2x)(x + -3) = 3 Reorder the terms: (1 + 2x)(-3 + x) = 3 Multiply (1 + 2x) * (-3 + x) (1(-3 + x) + 2x * (-3 + x)) = 3 ((-3 * 1 + x * 1) + 2x * (-3 + x)) = 3 ((-3 + 1x) + 2x * (-3 + x)) = 3 (-3 + 1x + (-3 * 2x + x * 2x)) = 3 (-3 + 1x + (-6x + 2x2)) = 3 Combine like terms: 1x + -6x = -5x (-3 + -5x + 2x2) = 3 Solving -3 + -5x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -3 + -5x + 2x2 = 3 + -3 Combine like terms: -3 + -3 = -6 -6 + -5x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -6 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -2.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.5x + x2 = 0 + 3 -2.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.5x + x2 = 3 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 = 3 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + -2.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -1.25 = 2.136000936 Simplifying x + -1.25 = 2.136000936 Reorder the terms: -1.25 + x = 2.136000936 Solving -1.25 + x = 2.136000936 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 = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.136000936 + 1.25 x = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 x = 3.386000936 Simplifying x = 3.386000936Subproblem 2
x + -1.25 = -2.136000936 Simplifying x + -1.25 = -2.136000936 Reorder the terms: -1.25 + x = -2.136000936 Solving -1.25 + x = -2.136000936 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 = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.136000936 + 1.25 x = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 x = -0.886000936 Simplifying x = -0.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.386000936, -0.886000936}
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