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Simplifying x = -0.2x2 + 100x + -9500 Reorder the terms: x = -9500 + 100x + -0.2x2 Solving x = -9500 + 100x + -0.2x2 Solving for variable 'x'. Reorder the terms: 9500 + x + -100x + 0.2x2 = -9500 + 100x + -0.2x2 + 9500 + -100x + 0.2x2 Combine like terms: x + -100x = -99x 9500 + -99x + 0.2x2 = -9500 + 100x + -0.2x2 + 9500 + -100x + 0.2x2 Reorder the terms: 9500 + -99x + 0.2x2 = -9500 + 9500 + 100x + -100x + -0.2x2 + 0.2x2 Combine like terms: -9500 + 9500 = 0 9500 + -99x + 0.2x2 = 0 + 100x + -100x + -0.2x2 + 0.2x2 9500 + -99x + 0.2x2 = 100x + -100x + -0.2x2 + 0.2x2 Combine like terms: 100x + -100x = 0 9500 + -99x + 0.2x2 = 0 + -0.2x2 + 0.2x2 9500 + -99x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 9500 + -99x + 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'. 47500 + -495x + x2 = 0 Move the constant term to the right: Add '-47500' to each side of the equation. 47500 + -495x + -47500 + x2 = 0 + -47500 Reorder the terms: 47500 + -47500 + -495x + x2 = 0 + -47500 Combine like terms: 47500 + -47500 = 0 0 + -495x + x2 = 0 + -47500 -495x + x2 = 0 + -47500 Combine like terms: 0 + -47500 = -47500 -495x + x2 = -47500 The x term is -495x. Take half its coefficient (-247.5). Square it (61256.25) and add it to both sides. Add '61256.25' to each side of the equation. -495x + 61256.25 + x2 = -47500 + 61256.25 Reorder the terms: 61256.25 + -495x + x2 = -47500 + 61256.25 Combine like terms: -47500 + 61256.25 = 13756.25 61256.25 + -495x + x2 = 13756.25 Factor a perfect square on the left side: (x + -247.5)(x + -247.5) = 13756.25 Calculate the square root of the right side: 117.287041057 Break this problem into two subproblems by setting (x + -247.5) equal to 117.287041057 and -117.287041057.Subproblem 1
x + -247.5 = 117.287041057 Simplifying x + -247.5 = 117.287041057 Reorder the terms: -247.5 + x = 117.287041057 Solving -247.5 + x = 117.287041057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '247.5' to each side of the equation. -247.5 + 247.5 + x = 117.287041057 + 247.5 Combine like terms: -247.5 + 247.5 = 0.0 0.0 + x = 117.287041057 + 247.5 x = 117.287041057 + 247.5 Combine like terms: 117.287041057 + 247.5 = 364.787041057 x = 364.787041057 Simplifying x = 364.787041057Subproblem 2
x + -247.5 = -117.287041057 Simplifying x + -247.5 = -117.287041057 Reorder the terms: -247.5 + x = -117.287041057 Solving -247.5 + x = -117.287041057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '247.5' to each side of the equation. -247.5 + 247.5 + x = -117.287041057 + 247.5 Combine like terms: -247.5 + 247.5 = 0.0 0.0 + x = -117.287041057 + 247.5 x = -117.287041057 + 247.5 Combine like terms: -117.287041057 + 247.5 = 130.212958943 x = 130.212958943 Simplifying x = 130.212958943Solution
The solution to the problem is based on the solutions from the subproblems. x = {364.787041057, 130.212958943}
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