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Simplifying 0.0000003923x2 + -0.246000405x + 0.00000001254 = 0 Reorder the terms: 0.00000001254 + -0.246000405x + 0.0000003923x2 = 0 Solving 0.00000001254 + -0.246000405x + 0.0000003923x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0000003923 the coefficient of the squared term: Divide each side by '0.0000003923'. 0.03196533265 + -627072.1514x + x2 = 0 Move the constant term to the right: Add '-0.03196533265' to each side of the equation. 0.03196533265 + -627072.1514x + -0.03196533265 + x2 = 0 + -0.03196533265 Reorder the terms: 0.03196533265 + -0.03196533265 + -627072.1514x + x2 = 0 + -0.03196533265 Combine like terms: 0.03196533265 + -0.03196533265 = 0.00000000000 0.00000000000 + -627072.1514x + x2 = 0 + -0.03196533265 -627072.1514x + x2 = 0 + -0.03196533265 Combine like terms: 0 + -0.03196533265 = -0.03196533265 -627072.1514x + x2 = -0.03196533265 The x term is -627072.1514x. Take half its coefficient (-313536.0757). Square it (98304870770) and add it to both sides. Add '98304870770' to each side of the equation. -627072.1514x + 98304870770 + x2 = -0.03196533265 + 98304870770 Reorder the terms: 98304870770 + -627072.1514x + x2 = -0.03196533265 + 98304870770 Combine like terms: -0.03196533265 + 98304870770 = 98304870769.96803466735 98304870770 + -627072.1514x + x2 = 98304870769.96803466735 Factor a perfect square on the left side: (x + -313536.0757)(x + -313536.0757) = 98304870769.96803466735 Calculate the square root of the right side: 313536.075707355 Break this problem into two subproblems by setting (x + -313536.0757) equal to 313536.075707355 and -313536.075707355.Subproblem 1
x + -313536.0757 = 313536.075707355 Simplifying x + -313536.0757 = 313536.075707355 Reorder the terms: -313536.0757 + x = 313536.075707355 Solving -313536.0757 + x = 313536.075707355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '313536.0757' to each side of the equation. -313536.0757 + 313536.0757 + x = 313536.075707355 + 313536.0757 Combine like terms: -313536.0757 + 313536.0757 = 0.0000 0.0000 + x = 313536.075707355 + 313536.0757 x = 313536.075707355 + 313536.0757 Combine like terms: 313536.075707355 + 313536.0757 = 627072.151407355 x = 627072.151407355 Simplifying x = 627072.151407355Subproblem 2
x + -313536.0757 = -313536.075707355 Simplifying x + -313536.0757 = -313536.075707355 Reorder the terms: -313536.0757 + x = -313536.075707355 Solving -313536.0757 + x = -313536.075707355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '313536.0757' to each side of the equation. -313536.0757 + 313536.0757 + x = -313536.075707355 + 313536.0757 Combine like terms: -313536.0757 + 313536.0757 = 0.0000 0.0000 + x = -313536.075707355 + 313536.0757 x = -313536.075707355 + 313536.0757 Combine like terms: -313536.075707355 + 313536.0757 = -0.000007355 x = -0.000007355 Simplifying x = -0.000007355Solution
The solution to the problem is based on the solutions from the subproblems. x = {627072.151407355, -0.000007355}
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