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Simplifying (x + 40)(x + 600) = 600 Reorder the terms: (40 + x)(x + 600) = 600 Reorder the terms: (40 + x)(600 + x) = 600 Multiply (40 + x) * (600 + x) (40(600 + x) + x(600 + x)) = 600 ((600 * 40 + x * 40) + x(600 + x)) = 600 ((24000 + 40x) + x(600 + x)) = 600 (24000 + 40x + (600 * x + x * x)) = 600 (24000 + 40x + (600x + x2)) = 600 Combine like terms: 40x + 600x = 640x (24000 + 640x + x2) = 600 Solving 24000 + 640x + x2 = 600 Solving for variable 'x'. Reorder the terms: 24000 + -600 + 640x + x2 = 600 + -600 Combine like terms: 24000 + -600 = 23400 23400 + 640x + x2 = 600 + -600 Combine like terms: 600 + -600 = 0 23400 + 640x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-23400' to each side of the equation. 23400 + 640x + -23400 + x2 = 0 + -23400 Reorder the terms: 23400 + -23400 + 640x + x2 = 0 + -23400 Combine like terms: 23400 + -23400 = 0 0 + 640x + x2 = 0 + -23400 640x + x2 = 0 + -23400 Combine like terms: 0 + -23400 = -23400 640x + x2 = -23400 The x term is 640x. Take half its coefficient (320). Square it (102400) and add it to both sides. Add '102400' to each side of the equation. 640x + 102400 + x2 = -23400 + 102400 Reorder the terms: 102400 + 640x + x2 = -23400 + 102400 Combine like terms: -23400 + 102400 = 79000 102400 + 640x + x2 = 79000 Factor a perfect square on the left side: (x + 320)(x + 320) = 79000 Calculate the square root of the right side: 281.069386451 Break this problem into two subproblems by setting (x + 320) equal to 281.069386451 and -281.069386451.Subproblem 1
x + 320 = 281.069386451 Simplifying x + 320 = 281.069386451 Reorder the terms: 320 + x = 281.069386451 Solving 320 + x = 281.069386451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-320' to each side of the equation. 320 + -320 + x = 281.069386451 + -320 Combine like terms: 320 + -320 = 0 0 + x = 281.069386451 + -320 x = 281.069386451 + -320 Combine like terms: 281.069386451 + -320 = -38.930613549 x = -38.930613549 Simplifying x = -38.930613549Subproblem 2
x + 320 = -281.069386451 Simplifying x + 320 = -281.069386451 Reorder the terms: 320 + x = -281.069386451 Solving 320 + x = -281.069386451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-320' to each side of the equation. 320 + -320 + x = -281.069386451 + -320 Combine like terms: 320 + -320 = 0 0 + x = -281.069386451 + -320 x = -281.069386451 + -320 Combine like terms: -281.069386451 + -320 = -601.069386451 x = -601.069386451 Simplifying x = -601.069386451Solution
The solution to the problem is based on the solutions from the subproblems. x = {-38.930613549, -601.069386451}
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