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Simplifying x2 + 800x + 57600 = 1200 Reorder the terms: 57600 + 800x + x2 = 1200 Solving 57600 + 800x + x2 = 1200 Solving for variable 'x'. Reorder the terms: 57600 + -1200 + 800x + x2 = 1200 + -1200 Combine like terms: 57600 + -1200 = 56400 56400 + 800x + x2 = 1200 + -1200 Combine like terms: 1200 + -1200 = 0 56400 + 800x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56400' to each side of the equation. 56400 + 800x + -56400 + x2 = 0 + -56400 Reorder the terms: 56400 + -56400 + 800x + x2 = 0 + -56400 Combine like terms: 56400 + -56400 = 0 0 + 800x + x2 = 0 + -56400 800x + x2 = 0 + -56400 Combine like terms: 0 + -56400 = -56400 800x + x2 = -56400 The x term is 800x. Take half its coefficient (400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. 800x + 160000 + x2 = -56400 + 160000 Reorder the terms: 160000 + 800x + x2 = -56400 + 160000 Combine like terms: -56400 + 160000 = 103600 160000 + 800x + x2 = 103600 Factor a perfect square on the left side: (x + 400)(x + 400) = 103600 Calculate the square root of the right side: 321.869538789 Break this problem into two subproblems by setting (x + 400) equal to 321.869538789 and -321.869538789.Subproblem 1
x + 400 = 321.869538789 Simplifying x + 400 = 321.869538789 Reorder the terms: 400 + x = 321.869538789 Solving 400 + x = 321.869538789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-400' to each side of the equation. 400 + -400 + x = 321.869538789 + -400 Combine like terms: 400 + -400 = 0 0 + x = 321.869538789 + -400 x = 321.869538789 + -400 Combine like terms: 321.869538789 + -400 = -78.130461211 x = -78.130461211 Simplifying x = -78.130461211Subproblem 2
x + 400 = -321.869538789 Simplifying x + 400 = -321.869538789 Reorder the terms: 400 + x = -321.869538789 Solving 400 + x = -321.869538789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-400' to each side of the equation. 400 + -400 + x = -321.869538789 + -400 Combine like terms: 400 + -400 = 0 0 + x = -321.869538789 + -400 x = -321.869538789 + -400 Combine like terms: -321.869538789 + -400 = -721.869538789 x = -721.869538789 Simplifying x = -721.869538789Solution
The solution to the problem is based on the solutions from the subproblems. x = {-78.130461211, -721.869538789}
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