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Simplifying 24 = (3 + -1x)(2 + -1x) Multiply (3 + -1x) * (2 + -1x) 24 = (3(2 + -1x) + -1x * (2 + -1x)) 24 = ((2 * 3 + -1x * 3) + -1x * (2 + -1x)) 24 = ((6 + -3x) + -1x * (2 + -1x)) 24 = (6 + -3x + (2 * -1x + -1x * -1x)) 24 = (6 + -3x + (-2x + 1x2)) Combine like terms: -3x + -2x = -5x 24 = (6 + -5x + 1x2) Solving 24 = 6 + -5x + 1x2 Solving for variable 'x'. Combine like terms: 24 + -6 = 18 18 + 5x + -1x2 = 6 + -5x + 1x2 + -6 + 5x + -1x2 Reorder the terms: 18 + 5x + -1x2 = 6 + -6 + -5x + 5x + 1x2 + -1x2 Combine like terms: 6 + -6 = 0 18 + 5x + -1x2 = 0 + -5x + 5x + 1x2 + -1x2 18 + 5x + -1x2 = -5x + 5x + 1x2 + -1x2 Combine like terms: -5x + 5x = 0 18 + 5x + -1x2 = 0 + 1x2 + -1x2 18 + 5x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 18 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + -5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -5x + x2 = 0 + 18 -5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -5x + x2 = 18 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 18 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 18 + 6.25 Combine like terms: 18 + 6.25 = 24.25 6.25 + -5x + x2 = 24.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -2.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -2.5 = 4.924428901 Simplifying x + -2.5 = 4.924428901 Reorder the terms: -2.5 + x = 4.924428901 Solving -2.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.924428901 + 2.5 x = 4.924428901 + 2.5 Combine like terms: 4.924428901 + 2.5 = 7.424428901 x = 7.424428901 Simplifying x = 7.424428901Subproblem 2
x + -2.5 = -4.924428901 Simplifying x + -2.5 = -4.924428901 Reorder the terms: -2.5 + x = -4.924428901 Solving -2.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.924428901 + 2.5 x = -4.924428901 + 2.5 Combine like terms: -4.924428901 + 2.5 = -2.424428901 x = -2.424428901 Simplifying x = -2.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.424428901, -2.424428901}
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