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Simplifying 9x + 3x(x + -1900) = 190000 Reorder the terms: 9x + 3x(-1900 + x) = 190000 9x + (-1900 * 3x + x * 3x) = 190000 9x + (-5700x + 3x2) = 190000 Combine like terms: 9x + -5700x = -5691x -5691x + 3x2 = 190000 Solving -5691x + 3x2 = 190000 Solving for variable 'x'. Reorder the terms: -190000 + -5691x + 3x2 = 190000 + -190000 Combine like terms: 190000 + -190000 = 0 -190000 + -5691x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -63333.33333 + -1897x + x2 = 0 Move the constant term to the right: Add '63333.33333' to each side of the equation. -63333.33333 + -1897x + 63333.33333 + x2 = 0 + 63333.33333 Reorder the terms: -63333.33333 + 63333.33333 + -1897x + x2 = 0 + 63333.33333 Combine like terms: -63333.33333 + 63333.33333 = 0.00000 0.00000 + -1897x + x2 = 0 + 63333.33333 -1897x + x2 = 0 + 63333.33333 Combine like terms: 0 + 63333.33333 = 63333.33333 -1897x + x2 = 63333.33333 The x term is -1897x. Take half its coefficient (-948.5). Square it (899652.25) and add it to both sides. Add '899652.25' to each side of the equation. -1897x + 899652.25 + x2 = 63333.33333 + 899652.25 Reorder the terms: 899652.25 + -1897x + x2 = 63333.33333 + 899652.25 Combine like terms: 63333.33333 + 899652.25 = 962985.58333 899652.25 + -1897x + x2 = 962985.58333 Factor a perfect square on the left side: (x + -948.5)(x + -948.5) = 962985.58333 Calculate the square root of the right side: 981.318288493 Break this problem into two subproblems by setting (x + -948.5) equal to 981.318288493 and -981.318288493.Subproblem 1
x + -948.5 = 981.318288493 Simplifying x + -948.5 = 981.318288493 Reorder the terms: -948.5 + x = 981.318288493 Solving -948.5 + x = 981.318288493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '948.5' to each side of the equation. -948.5 + 948.5 + x = 981.318288493 + 948.5 Combine like terms: -948.5 + 948.5 = 0.0 0.0 + x = 981.318288493 + 948.5 x = 981.318288493 + 948.5 Combine like terms: 981.318288493 + 948.5 = 1929.818288493 x = 1929.818288493 Simplifying x = 1929.818288493Subproblem 2
x + -948.5 = -981.318288493 Simplifying x + -948.5 = -981.318288493 Reorder the terms: -948.5 + x = -981.318288493 Solving -948.5 + x = -981.318288493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '948.5' to each side of the equation. -948.5 + 948.5 + x = -981.318288493 + 948.5 Combine like terms: -948.5 + 948.5 = 0.0 0.0 + x = -981.318288493 + 948.5 x = -981.318288493 + 948.5 Combine like terms: -981.318288493 + 948.5 = -32.818288493 x = -32.818288493 Simplifying x = -32.818288493Solution
The solution to the problem is based on the solutions from the subproblems. x = {1929.818288493, -32.818288493}
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