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Simplifying (-2x2 + 200x) + -1(x2 + 2x + 500) = 0 Reorder the terms: (200x + -2x2) + -1(x2 + 2x + 500) = 0 Remove parenthesis around (200x + -2x2) 200x + -2x2 + -1(x2 + 2x + 500) = 0 Reorder the terms: 200x + -2x2 + -1(500 + 2x + x2) = 0 200x + -2x2 + (500 * -1 + 2x * -1 + x2 * -1) = 0 200x + -2x2 + (-500 + -2x + -1x2) = 0 Reorder the terms: -500 + 200x + -2x + -2x2 + -1x2 = 0 Combine like terms: 200x + -2x = 198x -500 + 198x + -2x2 + -1x2 = 0 Combine like terms: -2x2 + -1x2 = -3x2 -500 + 198x + -3x2 = 0 Solving -500 + 198x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 166.6666667 + -66x + x2 = 0 Move the constant term to the right: Add '-166.6666667' to each side of the equation. 166.6666667 + -66x + -166.6666667 + x2 = 0 + -166.6666667 Reorder the terms: 166.6666667 + -166.6666667 + -66x + x2 = 0 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + -66x + x2 = 0 + -166.6666667 -66x + x2 = 0 + -166.6666667 Combine like terms: 0 + -166.6666667 = -166.6666667 -66x + x2 = -166.6666667 The x term is -66x. Take half its coefficient (-33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. -66x + 1089 + x2 = -166.6666667 + 1089 Reorder the terms: 1089 + -66x + x2 = -166.6666667 + 1089 Combine like terms: -166.6666667 + 1089 = 922.3333333 1089 + -66x + x2 = 922.3333333 Factor a perfect square on the left side: (x + -33)(x + -33) = 922.3333333 Calculate the square root of the right side: 30.369941279 Break this problem into two subproblems by setting (x + -33) equal to 30.369941279 and -30.369941279.Subproblem 1
x + -33 = 30.369941279 Simplifying x + -33 = 30.369941279 Reorder the terms: -33 + x = 30.369941279 Solving -33 + x = 30.369941279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = 30.369941279 + 33 Combine like terms: -33 + 33 = 0 0 + x = 30.369941279 + 33 x = 30.369941279 + 33 Combine like terms: 30.369941279 + 33 = 63.369941279 x = 63.369941279 Simplifying x = 63.369941279Subproblem 2
x + -33 = -30.369941279 Simplifying x + -33 = -30.369941279 Reorder the terms: -33 + x = -30.369941279 Solving -33 + x = -30.369941279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = -30.369941279 + 33 Combine like terms: -33 + 33 = 0 0 + x = -30.369941279 + 33 x = -30.369941279 + 33 Combine like terms: -30.369941279 + 33 = 2.630058721 x = 2.630058721 Simplifying x = 2.630058721Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.369941279, 2.630058721}
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