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Simplifying (x + 5)(x + -2) = 240 Reorder the terms: (5 + x)(x + -2) = 240 Reorder the terms: (5 + x)(-2 + x) = 240 Multiply (5 + x) * (-2 + x) (5(-2 + x) + x(-2 + x)) = 240 ((-2 * 5 + x * 5) + x(-2 + x)) = 240 ((-10 + 5x) + x(-2 + x)) = 240 (-10 + 5x + (-2 * x + x * x)) = 240 (-10 + 5x + (-2x + x2)) = 240 Combine like terms: 5x + -2x = 3x (-10 + 3x + x2) = 240 Solving -10 + 3x + x2 = 240 Solving for variable 'x'. Reorder the terms: -10 + -240 + 3x + x2 = 240 + -240 Combine like terms: -10 + -240 = -250 -250 + 3x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -250 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 3x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 3x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 3x + x2 = 0 + 250 3x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 3x + x2 = 250 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 = 250 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 250 + 2.25 Combine like terms: 250 + 2.25 = 252.25 2.25 + 3x + x2 = 252.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (x + 1.5) equal to 15.882380174 and -15.882380174.Subproblem 1
x + 1.5 = 15.882380174 Simplifying x + 1.5 = 15.882380174 Reorder the terms: 1.5 + x = 15.882380174 Solving 1.5 + x = 15.882380174 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 = 15.882380174 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.882380174 + -1.5 x = 15.882380174 + -1.5 Combine like terms: 15.882380174 + -1.5 = 14.382380174 x = 14.382380174 Simplifying x = 14.382380174Subproblem 2
x + 1.5 = -15.882380174 Simplifying x + 1.5 = -15.882380174 Reorder the terms: 1.5 + x = -15.882380174 Solving 1.5 + x = -15.882380174 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 = -15.882380174 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.882380174 + -1.5 x = -15.882380174 + -1.5 Combine like terms: -15.882380174 + -1.5 = -17.382380174 x = -17.382380174 Simplifying x = -17.382380174Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.382380174, -17.382380174}
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