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Simplifying x + x + -1(250) + 3x(x + -250) = 3500 Multiply -1 * 250 x + x + -250 + 3x(x + -250) = 3500 Reorder the terms: x + x + -250 + 3x(-250 + x) = 3500 x + x + -250 + (-250 * 3x + x * 3x) = 3500 x + x + -250 + (-750x + 3x2) = 3500 Reorder the terms: -250 + x + x + -750x + 3x2 = 3500 Combine like terms: x + x = 2x -250 + 2x + -750x + 3x2 = 3500 Combine like terms: 2x + -750x = -748x -250 + -748x + 3x2 = 3500 Solving -250 + -748x + 3x2 = 3500 Solving for variable 'x'. Reorder the terms: -250 + -3500 + -748x + 3x2 = 3500 + -3500 Combine like terms: -250 + -3500 = -3750 -3750 + -748x + 3x2 = 3500 + -3500 Combine like terms: 3500 + -3500 = 0 -3750 + -748x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1250 + -249.3333333x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + -249.3333333x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + -249.3333333x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + -249.3333333x + x2 = 0 + 1250 -249.3333333x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 -249.3333333x + x2 = 1250 The x term is -249.3333333x. Take half its coefficient (-124.6666667). Square it (15541.77779) and add it to both sides. Add '15541.77779' to each side of the equation. -249.3333333x + 15541.77779 + x2 = 1250 + 15541.77779 Reorder the terms: 15541.77779 + -249.3333333x + x2 = 1250 + 15541.77779 Combine like terms: 1250 + 15541.77779 = 16791.77779 15541.77779 + -249.3333333x + x2 = 16791.77779 Factor a perfect square on the left side: (x + -124.6666667)(x + -124.6666667) = 16791.77779 Calculate the square root of the right side: 129.583092223 Break this problem into two subproblems by setting (x + -124.6666667) equal to 129.583092223 and -129.583092223.Subproblem 1
x + -124.6666667 = 129.583092223 Simplifying x + -124.6666667 = 129.583092223 Reorder the terms: -124.6666667 + x = 129.583092223 Solving -124.6666667 + x = 129.583092223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '124.6666667' to each side of the equation. -124.6666667 + 124.6666667 + x = 129.583092223 + 124.6666667 Combine like terms: -124.6666667 + 124.6666667 = 0.0000000 0.0000000 + x = 129.583092223 + 124.6666667 x = 129.583092223 + 124.6666667 Combine like terms: 129.583092223 + 124.6666667 = 254.249758923 x = 254.249758923 Simplifying x = 254.249758923Subproblem 2
x + -124.6666667 = -129.583092223 Simplifying x + -124.6666667 = -129.583092223 Reorder the terms: -124.6666667 + x = -129.583092223 Solving -124.6666667 + x = -129.583092223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '124.6666667' to each side of the equation. -124.6666667 + 124.6666667 + x = -129.583092223 + 124.6666667 Combine like terms: -124.6666667 + 124.6666667 = 0.0000000 0.0000000 + x = -129.583092223 + 124.6666667 x = -129.583092223 + 124.6666667 Combine like terms: -129.583092223 + 124.6666667 = -4.916425523 x = -4.916425523 Simplifying x = -4.916425523Solution
The solution to the problem is based on the solutions from the subproblems. x = {254.249758923, -4.916425523}
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