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Simplifying -0.5x2 + 400x + -4400 = 0 Reorder the terms: -4400 + 400x + -0.5x2 = 0 Solving -4400 + 400x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 8800 + -800x + x2 = 0 Move the constant term to the right: Add '-8800' to each side of the equation. 8800 + -800x + -8800 + x2 = 0 + -8800 Reorder the terms: 8800 + -8800 + -800x + x2 = 0 + -8800 Combine like terms: 8800 + -8800 = 0 0 + -800x + x2 = 0 + -8800 -800x + x2 = 0 + -8800 Combine like terms: 0 + -8800 = -8800 -800x + x2 = -8800 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 = -8800 + 160000 Reorder the terms: 160000 + -800x + x2 = -8800 + 160000 Combine like terms: -8800 + 160000 = 151200 160000 + -800x + x2 = 151200 Factor a perfect square on the left side: (x + -400)(x + -400) = 151200 Calculate the square root of the right side: 388.844441904 Break this problem into two subproblems by setting (x + -400) equal to 388.844441904 and -388.844441904.Subproblem 1
x + -400 = 388.844441904 Simplifying x + -400 = 388.844441904 Reorder the terms: -400 + x = 388.844441904 Solving -400 + x = 388.844441904 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 = 388.844441904 + 400 Combine like terms: -400 + 400 = 0 0 + x = 388.844441904 + 400 x = 388.844441904 + 400 Combine like terms: 388.844441904 + 400 = 788.844441904 x = 788.844441904 Simplifying x = 788.844441904Subproblem 2
x + -400 = -388.844441904 Simplifying x + -400 = -388.844441904 Reorder the terms: -400 + x = -388.844441904 Solving -400 + x = -388.844441904 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 = -388.844441904 + 400 Combine like terms: -400 + 400 = 0 0 + x = -388.844441904 + 400 x = -388.844441904 + 400 Combine like terms: -388.844441904 + 400 = 11.155558096 x = 11.155558096 Simplifying x = 11.155558096Solution
The solution to the problem is based on the solutions from the subproblems. x = {788.844441904, 11.155558096}
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