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Simplifying (2x + -3)(x + 5) = 3 Reorder the terms: (-3 + 2x)(x + 5) = 3 Reorder the terms: (-3 + 2x)(5 + x) = 3 Multiply (-3 + 2x) * (5 + x) (-3(5 + x) + 2x * (5 + x)) = 3 ((5 * -3 + x * -3) + 2x * (5 + x)) = 3 ((-15 + -3x) + 2x * (5 + x)) = 3 (-15 + -3x + (5 * 2x + x * 2x)) = 3 (-15 + -3x + (10x + 2x2)) = 3 Combine like terms: -3x + 10x = 7x (-15 + 7x + 2x2) = 3 Solving -15 + 7x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -15 + -3 + 7x + 2x2 = 3 + -3 Combine like terms: -15 + -3 = -18 -18 + 7x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -18 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + 3.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 3.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 3.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3.5x + x2 = 0 + 9 3.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 3.5x + x2 = 9 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 9 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 9 + 3.0625 Combine like terms: 9 + 3.0625 = 12.0625 3.0625 + 3.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 1.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 1.75 = 3.473110997 Simplifying x + 1.75 = 3.473110997 Reorder the terms: 1.75 + x = 3.473110997 Solving 1.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.473110997 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.473110997 + -1.75 x = 3.473110997 + -1.75 Combine like terms: 3.473110997 + -1.75 = 1.723110997 x = 1.723110997 Simplifying x = 1.723110997Subproblem 2
x + 1.75 = -3.473110997 Simplifying x + 1.75 = -3.473110997 Reorder the terms: 1.75 + x = -3.473110997 Solving 1.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.473110997 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.473110997 + -1.75 x = -3.473110997 + -1.75 Combine like terms: -3.473110997 + -1.75 = -5.223110997 x = -5.223110997 Simplifying x = -5.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.723110997, -5.223110997}
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