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Simplifying (2x + -3)(x + 8) = 184 Reorder the terms: (-3 + 2x)(x + 8) = 184 Reorder the terms: (-3 + 2x)(8 + x) = 184 Multiply (-3 + 2x) * (8 + x) (-3(8 + x) + 2x * (8 + x)) = 184 ((8 * -3 + x * -3) + 2x * (8 + x)) = 184 ((-24 + -3x) + 2x * (8 + x)) = 184 (-24 + -3x + (8 * 2x + x * 2x)) = 184 (-24 + -3x + (16x + 2x2)) = 184 Combine like terms: -3x + 16x = 13x (-24 + 13x + 2x2) = 184 Solving -24 + 13x + 2x2 = 184 Solving for variable 'x'. Reorder the terms: -24 + -184 + 13x + 2x2 = 184 + -184 Combine like terms: -24 + -184 = -208 -208 + 13x + 2x2 = 184 + -184 Combine like terms: 184 + -184 = 0 -208 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -104 + 6.5x + x2 = 0 Move the constant term to the right: Add '104' to each side of the equation. -104 + 6.5x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 6.5x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 6.5x + x2 = 0 + 104 6.5x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 6.5x + x2 = 104 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 104 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 104 + 10.5625 Combine like terms: 104 + 10.5625 = 114.5625 10.5625 + 6.5x + x2 = 114.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 114.5625 Calculate the square root of the right side: 10.703387314 Break this problem into two subproblems by setting (x + 3.25) equal to 10.703387314 and -10.703387314.Subproblem 1
x + 3.25 = 10.703387314 Simplifying x + 3.25 = 10.703387314 Reorder the terms: 3.25 + x = 10.703387314 Solving 3.25 + x = 10.703387314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 10.703387314 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 10.703387314 + -3.25 x = 10.703387314 + -3.25 Combine like terms: 10.703387314 + -3.25 = 7.453387314 x = 7.453387314 Simplifying x = 7.453387314Subproblem 2
x + 3.25 = -10.703387314 Simplifying x + 3.25 = -10.703387314 Reorder the terms: 3.25 + x = -10.703387314 Solving 3.25 + x = -10.703387314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -10.703387314 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -10.703387314 + -3.25 x = -10.703387314 + -3.25 Combine like terms: -10.703387314 + -3.25 = -13.953387314 x = -13.953387314 Simplifying x = -13.953387314Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.453387314, -13.953387314}
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