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Simplifying (2x + 1)(x + -3) = 44 Reorder the terms: (1 + 2x)(x + -3) = 44 Reorder the terms: (1 + 2x)(-3 + x) = 44 Multiply (1 + 2x) * (-3 + x) (1(-3 + x) + 2x * (-3 + x)) = 44 ((-3 * 1 + x * 1) + 2x * (-3 + x)) = 44 ((-3 + 1x) + 2x * (-3 + x)) = 44 (-3 + 1x + (-3 * 2x + x * 2x)) = 44 (-3 + 1x + (-6x + 2x2)) = 44 Combine like terms: 1x + -6x = -5x (-3 + -5x + 2x2) = 44 Solving -3 + -5x + 2x2 = 44 Solving for variable 'x'. Reorder the terms: -3 + -44 + -5x + 2x2 = 44 + -44 Combine like terms: -3 + -44 = -47 -47 + -5x + 2x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -47 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + -2.5x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + -2.5x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + -2.5x + x2 = 0 + 23.5 -2.5x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 -2.5x + x2 = 23.5 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 = 23.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 23.5 + 1.5625 Combine like terms: 23.5 + 1.5625 = 25.0625 1.5625 + -2.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + -1.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x + -1.25 = 5.006246099 Simplifying x + -1.25 = 5.006246099 Reorder the terms: -1.25 + x = 5.006246099 Solving -1.25 + x = 5.006246099 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 = 5.006246099 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 5.006246099 + 1.25 x = 5.006246099 + 1.25 Combine like terms: 5.006246099 + 1.25 = 6.256246099 x = 6.256246099 Simplifying x = 6.256246099Subproblem 2
x + -1.25 = -5.006246099 Simplifying x + -1.25 = -5.006246099 Reorder the terms: -1.25 + x = -5.006246099 Solving -1.25 + x = -5.006246099 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 = -5.006246099 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -5.006246099 + 1.25 x = -5.006246099 + 1.25 Combine like terms: -5.006246099 + 1.25 = -3.756246099 x = -3.756246099 Simplifying x = -3.756246099Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.256246099, -3.756246099}
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