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Simplifying (x + 4)(x + -2) = 440 Reorder the terms: (4 + x)(x + -2) = 440 Reorder the terms: (4 + x)(-2 + x) = 440 Multiply (4 + x) * (-2 + x) (4(-2 + x) + x(-2 + x)) = 440 ((-2 * 4 + x * 4) + x(-2 + x)) = 440 ((-8 + 4x) + x(-2 + x)) = 440 (-8 + 4x + (-2 * x + x * x)) = 440 (-8 + 4x + (-2x + x2)) = 440 Combine like terms: 4x + -2x = 2x (-8 + 2x + x2) = 440 Solving -8 + 2x + x2 = 440 Solving for variable 'x'. Reorder the terms: -8 + -440 + 2x + x2 = 440 + -440 Combine like terms: -8 + -440 = -448 -448 + 2x + x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -448 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '448' to each side of the equation. -448 + 2x + 448 + x2 = 0 + 448 Reorder the terms: -448 + 448 + 2x + x2 = 0 + 448 Combine like terms: -448 + 448 = 0 0 + 2x + x2 = 0 + 448 2x + x2 = 0 + 448 Combine like terms: 0 + 448 = 448 2x + x2 = 448 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 448 + 1 Reorder the terms: 1 + 2x + x2 = 448 + 1 Combine like terms: 448 + 1 = 449 1 + 2x + x2 = 449 Factor a perfect square on the left side: (x + 1)(x + 1) = 449 Calculate the square root of the right side: 21.1896201 Break this problem into two subproblems by setting (x + 1) equal to 21.1896201 and -21.1896201.Subproblem 1
x + 1 = 21.1896201 Simplifying x + 1 = 21.1896201 Reorder the terms: 1 + x = 21.1896201 Solving 1 + x = 21.1896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 21.1896201 + -1 Combine like terms: 1 + -1 = 0 0 + x = 21.1896201 + -1 x = 21.1896201 + -1 Combine like terms: 21.1896201 + -1 = 20.1896201 x = 20.1896201 Simplifying x = 20.1896201Subproblem 2
x + 1 = -21.1896201 Simplifying x + 1 = -21.1896201 Reorder the terms: 1 + x = -21.1896201 Solving 1 + x = -21.1896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -21.1896201 + -1 Combine like terms: 1 + -1 = 0 0 + x = -21.1896201 + -1 x = -21.1896201 + -1 Combine like terms: -21.1896201 + -1 = -22.1896201 x = -22.1896201 Simplifying x = -22.1896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.1896201, -22.1896201}
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