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Simplifying 1100 = -0.2x2 + 140x + -3000 Reorder the terms: 1100 = -3000 + 140x + -0.2x2 Solving 1100 = -3000 + 140x + -0.2x2 Solving for variable 'x'. Combine like terms: 1100 + 3000 = 4100 4100 + -140x + 0.2x2 = -3000 + 140x + -0.2x2 + 3000 + -140x + 0.2x2 Reorder the terms: 4100 + -140x + 0.2x2 = -3000 + 3000 + 140x + -140x + -0.2x2 + 0.2x2 Combine like terms: -3000 + 3000 = 0 4100 + -140x + 0.2x2 = 0 + 140x + -140x + -0.2x2 + 0.2x2 4100 + -140x + 0.2x2 = 140x + -140x + -0.2x2 + 0.2x2 Combine like terms: 140x + -140x = 0 4100 + -140x + 0.2x2 = 0 + -0.2x2 + 0.2x2 4100 + -140x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 4100 + -140x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 20500 + -700x + x2 = 0 Move the constant term to the right: Add '-20500' to each side of the equation. 20500 + -700x + -20500 + x2 = 0 + -20500 Reorder the terms: 20500 + -20500 + -700x + x2 = 0 + -20500 Combine like terms: 20500 + -20500 = 0 0 + -700x + x2 = 0 + -20500 -700x + x2 = 0 + -20500 Combine like terms: 0 + -20500 = -20500 -700x + x2 = -20500 The x term is -700x. Take half its coefficient (-350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. -700x + 122500 + x2 = -20500 + 122500 Reorder the terms: 122500 + -700x + x2 = -20500 + 122500 Combine like terms: -20500 + 122500 = 102000 122500 + -700x + x2 = 102000 Factor a perfect square on the left side: (x + -350)(x + -350) = 102000 Calculate the square root of the right side: 319.374388453 Break this problem into two subproblems by setting (x + -350) equal to 319.374388453 and -319.374388453.Subproblem 1
x + -350 = 319.374388453 Simplifying x + -350 = 319.374388453 Reorder the terms: -350 + x = 319.374388453 Solving -350 + x = 319.374388453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = 319.374388453 + 350 Combine like terms: -350 + 350 = 0 0 + x = 319.374388453 + 350 x = 319.374388453 + 350 Combine like terms: 319.374388453 + 350 = 669.374388453 x = 669.374388453 Simplifying x = 669.374388453Subproblem 2
x + -350 = -319.374388453 Simplifying x + -350 = -319.374388453 Reorder the terms: -350 + x = -319.374388453 Solving -350 + x = -319.374388453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = -319.374388453 + 350 Combine like terms: -350 + 350 = 0 0 + x = -319.374388453 + 350 x = -319.374388453 + 350 Combine like terms: -319.374388453 + 350 = 30.625611547 x = 30.625611547 Simplifying x = 30.625611547Solution
The solution to the problem is based on the solutions from the subproblems. x = {669.374388453, 30.625611547}
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