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Simplifying 0.0000233320x2 + -0.246023951x + 0.00000061861 = 0 Reorder the terms: 0.00000061861 + -0.246023951x + 0.0000233320x2 = 0 Solving 0.00000061861 + -0.246023951x + 0.0000233320x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0000233320 the coefficient of the squared term: Divide each side by '0.0000233320'. 0.02651337219 + -10544.48616x + x2 = 0 Move the constant term to the right: Add '-0.02651337219' to each side of the equation. 0.02651337219 + -10544.48616x + -0.02651337219 + x2 = 0 + -0.02651337219 Reorder the terms: 0.02651337219 + -0.02651337219 + -10544.48616x + x2 = 0 + -0.02651337219 Combine like terms: 0.02651337219 + -0.02651337219 = 0.00000000000 0.00000000000 + -10544.48616x + x2 = 0 + -0.02651337219 -10544.48616x + x2 = 0 + -0.02651337219 Combine like terms: 0 + -0.02651337219 = -0.02651337219 -10544.48616x + x2 = -0.02651337219 The x term is -10544.48616x. Take half its coefficient (-5272.24308). Square it (27796547.09) and add it to both sides. Add '27796547.09' to each side of the equation. -10544.48616x + 27796547.09 + x2 = -0.02651337219 + 27796547.09 Reorder the terms: 27796547.09 + -10544.48616x + x2 = -0.02651337219 + 27796547.09 Combine like terms: -0.02651337219 + 27796547.09 = 27796547.06348662781 27796547.09 + -10544.48616x + x2 = 27796547.06348662781 Factor a perfect square on the left side: (x + -5272.24308)(x + -5272.24308) = 27796547.06348662781 Calculate the square root of the right side: 5272.243077049 Break this problem into two subproblems by setting (x + -5272.24308) equal to 5272.243077049 and -5272.243077049.Subproblem 1
x + -5272.24308 = 5272.243077049 Simplifying x + -5272.24308 = 5272.243077049 Reorder the terms: -5272.24308 + x = 5272.243077049 Solving -5272.24308 + x = 5272.243077049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5272.24308' to each side of the equation. -5272.24308 + 5272.24308 + x = 5272.243077049 + 5272.24308 Combine like terms: -5272.24308 + 5272.24308 = 0.00000 0.00000 + x = 5272.243077049 + 5272.24308 x = 5272.243077049 + 5272.24308 Combine like terms: 5272.243077049 + 5272.24308 = 10544.486157049 x = 10544.486157049 Simplifying x = 10544.486157049Subproblem 2
x + -5272.24308 = -5272.243077049 Simplifying x + -5272.24308 = -5272.243077049 Reorder the terms: -5272.24308 + x = -5272.243077049 Solving -5272.24308 + x = -5272.243077049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5272.24308' to each side of the equation. -5272.24308 + 5272.24308 + x = -5272.243077049 + 5272.24308 Combine like terms: -5272.24308 + 5272.24308 = 0.00000 0.00000 + x = -5272.243077049 + 5272.24308 x = -5272.243077049 + 5272.24308 Combine like terms: -5272.243077049 + 5272.24308 = 0.000002951 x = 0.000002951 Simplifying x = 0.000002951Solution
The solution to the problem is based on the solutions from the subproblems. x = {10544.486157049, 0.000002951}
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