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Simplifying 3x2 + -90 + 2005x + x = 9999999 Reorder the terms: -90 + 2005x + x + 3x2 = 9999999 Combine like terms: 2005x + x = 2006x -90 + 2006x + 3x2 = 9999999 Solving -90 + 2006x + 3x2 = 9999999 Solving for variable 'x'. Reorder the terms: -90 + -9999999 + 2006x + 3x2 = 9999999 + -9999999 Combine like terms: -90 + -9999999 = -10000089 -10000089 + 2006x + 3x2 = 9999999 + -9999999 Combine like terms: 9999999 + -9999999 = 0 -10000089 + 2006x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3333363 + 668.6666667x + x2 = 0 Move the constant term to the right: Add '3333363' to each side of the equation. -3333363 + 668.6666667x + 3333363 + x2 = 0 + 3333363 Reorder the terms: -3333363 + 3333363 + 668.6666667x + x2 = 0 + 3333363 Combine like terms: -3333363 + 3333363 = 0 0 + 668.6666667x + x2 = 0 + 3333363 668.6666667x + x2 = 0 + 3333363 Combine like terms: 0 + 3333363 = 3333363 668.6666667x + x2 = 3333363 The x term is 668.6666667x. Take half its coefficient (334.3333334). Square it (111778.7778) and add it to both sides. Add '111778.7778' to each side of the equation. 668.6666667x + 111778.7778 + x2 = 3333363 + 111778.7778 Reorder the terms: 111778.7778 + 668.6666667x + x2 = 3333363 + 111778.7778 Combine like terms: 3333363 + 111778.7778 = 3445141.7778 111778.7778 + 668.6666667x + x2 = 3445141.7778 Factor a perfect square on the left side: (x + 334.3333334)(x + 334.3333334) = 3445141.7778 Calculate the square root of the right side: 1856.109311921 Break this problem into two subproblems by setting (x + 334.3333334) equal to 1856.109311921 and -1856.109311921.Subproblem 1
x + 334.3333334 = 1856.109311921 Simplifying x + 334.3333334 = 1856.109311921 Reorder the terms: 334.3333334 + x = 1856.109311921 Solving 334.3333334 + x = 1856.109311921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-334.3333334' to each side of the equation. 334.3333334 + -334.3333334 + x = 1856.109311921 + -334.3333334 Combine like terms: 334.3333334 + -334.3333334 = 0.0000000 0.0000000 + x = 1856.109311921 + -334.3333334 x = 1856.109311921 + -334.3333334 Combine like terms: 1856.109311921 + -334.3333334 = 1521.775978521 x = 1521.775978521 Simplifying x = 1521.775978521Subproblem 2
x + 334.3333334 = -1856.109311921 Simplifying x + 334.3333334 = -1856.109311921 Reorder the terms: 334.3333334 + x = -1856.109311921 Solving 334.3333334 + x = -1856.109311921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-334.3333334' to each side of the equation. 334.3333334 + -334.3333334 + x = -1856.109311921 + -334.3333334 Combine like terms: 334.3333334 + -334.3333334 = 0.0000000 0.0000000 + x = -1856.109311921 + -334.3333334 x = -1856.109311921 + -334.3333334 Combine like terms: -1856.109311921 + -334.3333334 = -2190.442645321 x = -2190.442645321 Simplifying x = -2190.442645321Solution
The solution to the problem is based on the solutions from the subproblems. x = {1521.775978521, -2190.442645321}
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