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Simplifying -24673.20799626468x2 + 314.019418x + 1 = 0 Reorder the terms: 1 + 314.019418x + -24673.20799626468x2 = 0 Solving 1 + 314.019418x + -24673.20799626468x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -24673.20799626468 the coefficient of the squared term: Divide each side by '-24673.20799626468'. -0.00004052979248 + -0.01272714185x + x2 = 0 Move the constant term to the right: Add '0.00004052979248' to each side of the equation. -0.00004052979248 + -0.01272714185x + 0.00004052979248 + x2 = 0 + 0.00004052979248 Reorder the terms: -0.00004052979248 + 0.00004052979248 + -0.01272714185x + x2 = 0 + 0.00004052979248 Combine like terms: -0.00004052979248 + 0.00004052979248 = 0.00000000000000 0.00000000000000 + -0.01272714185x + x2 = 0 + 0.00004052979248 -0.01272714185x + x2 = 0 + 0.00004052979248 Combine like terms: 0 + 0.00004052979248 = 0.00004052979248 -0.01272714185x + x2 = 0.00004052979248 The x term is -0.01272714185x. Take half its coefficient (-0.006363570925). Square it (0.00004049503492) and add it to both sides. Add '0.00004049503492' to each side of the equation. -0.01272714185x + 0.00004049503492 + x2 = 0.00004052979248 + 0.00004049503492 Reorder the terms: 0.00004049503492 + -0.01272714185x + x2 = 0.00004052979248 + 0.00004049503492 Combine like terms: 0.00004052979248 + 0.00004049503492 = 0.0000810248274 0.00004049503492 + -0.01272714185x + x2 = 0.0000810248274 Factor a perfect square on the left side: (x + -0.006363570925)(x + -0.006363570925) = 0.0000810248274 Calculate the square root of the right side: 0.009001379 Break this problem into two subproblems by setting (x + -0.006363570925) equal to 0.009001379 and -0.009001379.Subproblem 1
x + -0.006363570925 = 0.009001379 Simplifying x + -0.006363570925 = 0.009001379 Reorder the terms: -0.006363570925 + x = 0.009001379 Solving -0.006363570925 + x = 0.009001379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006363570925' to each side of the equation. -0.006363570925 + 0.006363570925 + x = 0.009001379 + 0.006363570925 Combine like terms: -0.006363570925 + 0.006363570925 = 0.000000000000 0.000000000000 + x = 0.009001379 + 0.006363570925 x = 0.009001379 + 0.006363570925 Combine like terms: 0.009001379 + 0.006363570925 = 0.015364949925 x = 0.015364949925 Simplifying x = 0.015364949925Subproblem 2
x + -0.006363570925 = -0.009001379 Simplifying x + -0.006363570925 = -0.009001379 Reorder the terms: -0.006363570925 + x = -0.009001379 Solving -0.006363570925 + x = -0.009001379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006363570925' to each side of the equation. -0.006363570925 + 0.006363570925 + x = -0.009001379 + 0.006363570925 Combine like terms: -0.006363570925 + 0.006363570925 = 0.000000000000 0.000000000000 + x = -0.009001379 + 0.006363570925 x = -0.009001379 + 0.006363570925 Combine like terms: -0.009001379 + 0.006363570925 = -0.002637808075 x = -0.002637808075 Simplifying x = -0.002637808075Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.015364949925, -0.002637808075}
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