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Simplifying (62500 + 800x + x2) = 0 Remove parenthesis around (62500 + 800x + x2) 62500 + 800x + x2 = 0 Solving 62500 + 800x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-62500' to each side of the equation. 62500 + 800x + -62500 + x2 = 0 + -62500 Reorder the terms: 62500 + -62500 + 800x + x2 = 0 + -62500 Combine like terms: 62500 + -62500 = 0 0 + 800x + x2 = 0 + -62500 800x + x2 = 0 + -62500 Combine like terms: 0 + -62500 = -62500 800x + x2 = -62500 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 = -62500 + 160000 Reorder the terms: 160000 + 800x + x2 = -62500 + 160000 Combine like terms: -62500 + 160000 = 97500 160000 + 800x + x2 = 97500 Factor a perfect square on the left side: (x + 400)(x + 400) = 97500 Calculate the square root of the right side: 312.24989992 Break this problem into two subproblems by setting (x + 400) equal to 312.24989992 and -312.24989992.Subproblem 1
x + 400 = 312.24989992 Simplifying x + 400 = 312.24989992 Reorder the terms: 400 + x = 312.24989992 Solving 400 + x = 312.24989992 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 = 312.24989992 + -400 Combine like terms: 400 + -400 = 0 0 + x = 312.24989992 + -400 x = 312.24989992 + -400 Combine like terms: 312.24989992 + -400 = -87.75010008 x = -87.75010008 Simplifying x = -87.75010008Subproblem 2
x + 400 = -312.24989992 Simplifying x + 400 = -312.24989992 Reorder the terms: 400 + x = -312.24989992 Solving 400 + x = -312.24989992 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 = -312.24989992 + -400 Combine like terms: 400 + -400 = 0 0 + x = -312.24989992 + -400 x = -312.24989992 + -400 Combine like terms: -312.24989992 + -400 = -712.24989992 x = -712.24989992 Simplifying x = -712.24989992Solution
The solution to the problem is based on the solutions from the subproblems. x = {-87.75010008, -712.24989992}
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