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Simplifying (x + 10)(x + -6) = 360 Reorder the terms: (10 + x)(x + -6) = 360 Reorder the terms: (10 + x)(-6 + x) = 360 Multiply (10 + x) * (-6 + x) (10(-6 + x) + x(-6 + x)) = 360 ((-6 * 10 + x * 10) + x(-6 + x)) = 360 ((-60 + 10x) + x(-6 + x)) = 360 (-60 + 10x + (-6 * x + x * x)) = 360 (-60 + 10x + (-6x + x2)) = 360 Combine like terms: 10x + -6x = 4x (-60 + 4x + x2) = 360 Solving -60 + 4x + x2 = 360 Solving for variable 'x'. Reorder the terms: -60 + -360 + 4x + x2 = 360 + -360 Combine like terms: -60 + -360 = -420 -420 + 4x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -420 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '420' to each side of the equation. -420 + 4x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + 4x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 4x + x2 = 0 + 420 4x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 4x + x2 = 420 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 420 + 4 Reorder the terms: 4 + 4x + x2 = 420 + 4 Combine like terms: 420 + 4 = 424 4 + 4x + x2 = 424 Factor a perfect square on the left side: (x + 2)(x + 2) = 424 Calculate the square root of the right side: 20.591260282 Break this problem into two subproblems by setting (x + 2) equal to 20.591260282 and -20.591260282.Subproblem 1
x + 2 = 20.591260282 Simplifying x + 2 = 20.591260282 Reorder the terms: 2 + x = 20.591260282 Solving 2 + x = 20.591260282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 20.591260282 + -2 Combine like terms: 2 + -2 = 0 0 + x = 20.591260282 + -2 x = 20.591260282 + -2 Combine like terms: 20.591260282 + -2 = 18.591260282 x = 18.591260282 Simplifying x = 18.591260282Subproblem 2
x + 2 = -20.591260282 Simplifying x + 2 = -20.591260282 Reorder the terms: 2 + x = -20.591260282 Solving 2 + x = -20.591260282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -20.591260282 + -2 Combine like terms: 2 + -2 = 0 0 + x = -20.591260282 + -2 x = -20.591260282 + -2 Combine like terms: -20.591260282 + -2 = -22.591260282 x = -22.591260282 Simplifying x = -22.591260282Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.591260282, -22.591260282}
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