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Simplifying (x + 5)(3 + -1x) = x + -2 Reorder the terms: (5 + x)(3 + -1x) = x + -2 Multiply (5 + x) * (3 + -1x) (5(3 + -1x) + x(3 + -1x)) = x + -2 ((3 * 5 + -1x * 5) + x(3 + -1x)) = x + -2 ((15 + -5x) + x(3 + -1x)) = x + -2 (15 + -5x + (3 * x + -1x * x)) = x + -2 (15 + -5x + (3x + -1x2)) = x + -2 Combine like terms: -5x + 3x = -2x (15 + -2x + -1x2) = x + -2 Reorder the terms: 15 + -2x + -1x2 = -2 + x Solving 15 + -2x + -1x2 = -2 + x Solving for variable 'x'. Reorder the terms: 15 + 2 + -2x + -1x + -1x2 = -2 + x + 2 + -1x Combine like terms: 15 + 2 = 17 17 + -2x + -1x + -1x2 = -2 + x + 2 + -1x Combine like terms: -2x + -1x = -3x 17 + -3x + -1x2 = -2 + x + 2 + -1x Reorder the terms: 17 + -3x + -1x2 = -2 + 2 + x + -1x Combine like terms: -2 + 2 = 0 17 + -3x + -1x2 = 0 + x + -1x 17 + -3x + -1x2 = x + -1x Combine like terms: x + -1x = 0 17 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + 3x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 3x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 3x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 3x + x2 = 0 + 17 3x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 3x + x2 = 17 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 17 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 17 + 2.25 Combine like terms: 17 + 2.25 = 19.25 2.25 + 3x + x2 = 19.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 1.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 1.5 = 4.387482194 Simplifying x + 1.5 = 4.387482194 Reorder the terms: 1.5 + x = 4.387482194 Solving 1.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.387482194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.387482194 + -1.5 x = 4.387482194 + -1.5 Combine like terms: 4.387482194 + -1.5 = 2.887482194 x = 2.887482194 Simplifying x = 2.887482194Subproblem 2
x + 1.5 = -4.387482194 Simplifying x + 1.5 = -4.387482194 Reorder the terms: 1.5 + x = -4.387482194 Solving 1.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.387482194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.387482194 + -1.5 x = -4.387482194 + -1.5 Combine like terms: -4.387482194 + -1.5 = -5.887482194 x = -5.887482194 Simplifying x = -5.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.887482194, -5.887482194}
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