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Simplifying 0.9x + 0.11x(5000 + -1x) = 487 0.9x + (5000 * 0.11x + -1x * 0.11x) = 487 0.9x + (550x + -0.11x2) = 487 Combine like terms: 0.9x + 550x = 550.9x 550.9x + -0.11x2 = 487 Solving 550.9x + -0.11x2 = 487 Solving for variable 'x'. Reorder the terms: -487 + 550.9x + -0.11x2 = 487 + -487 Combine like terms: 487 + -487 = 0 -487 + 550.9x + -0.11x2 = 0 Begin completing the square. Divide all terms by -0.11 the coefficient of the squared term: Divide each side by '-0.11'. 4427.272727 + -5008.181818x + x2 = 0 Move the constant term to the right: Add '-4427.272727' to each side of the equation. 4427.272727 + -5008.181818x + -4427.272727 + x2 = 0 + -4427.272727 Reorder the terms: 4427.272727 + -4427.272727 + -5008.181818x + x2 = 0 + -4427.272727 Combine like terms: 4427.272727 + -4427.272727 = 0.000000 0.000000 + -5008.181818x + x2 = 0 + -4427.272727 -5008.181818x + x2 = 0 + -4427.272727 Combine like terms: 0 + -4427.272727 = -4427.272727 -5008.181818x + x2 = -4427.272727 The x term is -5008.181818x. Take half its coefficient (-2504.090909). Square it (6270471.281) and add it to both sides. Add '6270471.281' to each side of the equation. -5008.181818x + 6270471.281 + x2 = -4427.272727 + 6270471.281 Reorder the terms: 6270471.281 + -5008.181818x + x2 = -4427.272727 + 6270471.281 Combine like terms: -4427.272727 + 6270471.281 = 6266044.008273 6270471.281 + -5008.181818x + x2 = 6266044.008273 Factor a perfect square on the left side: (x + -2504.090909)(x + -2504.090909) = 6266044.008273 Calculate the square root of the right side: 2503.206745012 Break this problem into two subproblems by setting (x + -2504.090909) equal to 2503.206745012 and -2503.206745012.Subproblem 1
x + -2504.090909 = 2503.206745012 Simplifying x + -2504.090909 = 2503.206745012 Reorder the terms: -2504.090909 + x = 2503.206745012 Solving -2504.090909 + x = 2503.206745012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2504.090909' to each side of the equation. -2504.090909 + 2504.090909 + x = 2503.206745012 + 2504.090909 Combine like terms: -2504.090909 + 2504.090909 = 0.000000 0.000000 + x = 2503.206745012 + 2504.090909 x = 2503.206745012 + 2504.090909 Combine like terms: 2503.206745012 + 2504.090909 = 5007.297654012 x = 5007.297654012 Simplifying x = 5007.297654012Subproblem 2
x + -2504.090909 = -2503.206745012 Simplifying x + -2504.090909 = -2503.206745012 Reorder the terms: -2504.090909 + x = -2503.206745012 Solving -2504.090909 + x = -2503.206745012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2504.090909' to each side of the equation. -2504.090909 + 2504.090909 + x = -2503.206745012 + 2504.090909 Combine like terms: -2504.090909 + 2504.090909 = 0.000000 0.000000 + x = -2503.206745012 + 2504.090909 x = -2503.206745012 + 2504.090909 Combine like terms: -2503.206745012 + 2504.090909 = 0.884163988 x = 0.884163988 Simplifying x = 0.884163988Solution
The solution to the problem is based on the solutions from the subproblems. x = {5007.297654012, 0.884163988}
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