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Simplifying 20.2764x2 + -140.73x + 125.38 = 0 Reorder the terms: 125.38 + -140.73x + 20.2764x2 = 0 Solving 125.38 + -140.73x + 20.2764x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20.2764 the coefficient of the squared term: Divide each side by '20.2764'. 6.18354343 + -6.940581168x + x2 = 0 Move the constant term to the right: Add '-6.18354343' to each side of the equation. 6.18354343 + -6.940581168x + -6.18354343 + x2 = 0 + -6.18354343 Reorder the terms: 6.18354343 + -6.18354343 + -6.940581168x + x2 = 0 + -6.18354343 Combine like terms: 6.18354343 + -6.18354343 = 0.00000000 0.00000000 + -6.940581168x + x2 = 0 + -6.18354343 -6.940581168x + x2 = 0 + -6.18354343 Combine like terms: 0 + -6.18354343 = -6.18354343 -6.940581168x + x2 = -6.18354343 The x term is -6.940581168x. Take half its coefficient (-3.470290584). Square it (12.04291674) and add it to both sides. Add '12.04291674' to each side of the equation. -6.940581168x + 12.04291674 + x2 = -6.18354343 + 12.04291674 Reorder the terms: 12.04291674 + -6.940581168x + x2 = -6.18354343 + 12.04291674 Combine like terms: -6.18354343 + 12.04291674 = 5.85937331 12.04291674 + -6.940581168x + x2 = 5.85937331 Factor a perfect square on the left side: (x + -3.470290584)(x + -3.470290584) = 5.85937331 Calculate the square root of the right side: 2.420614242 Break this problem into two subproblems by setting (x + -3.470290584) equal to 2.420614242 and -2.420614242.Subproblem 1
x + -3.470290584 = 2.420614242 Simplifying x + -3.470290584 = 2.420614242 Reorder the terms: -3.470290584 + x = 2.420614242 Solving -3.470290584 + x = 2.420614242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.470290584' to each side of the equation. -3.470290584 + 3.470290584 + x = 2.420614242 + 3.470290584 Combine like terms: -3.470290584 + 3.470290584 = 0.000000000 0.000000000 + x = 2.420614242 + 3.470290584 x = 2.420614242 + 3.470290584 Combine like terms: 2.420614242 + 3.470290584 = 5.890904826 x = 5.890904826 Simplifying x = 5.890904826Subproblem 2
x + -3.470290584 = -2.420614242 Simplifying x + -3.470290584 = -2.420614242 Reorder the terms: -3.470290584 + x = -2.420614242 Solving -3.470290584 + x = -2.420614242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.470290584' to each side of the equation. -3.470290584 + 3.470290584 + x = -2.420614242 + 3.470290584 Combine like terms: -3.470290584 + 3.470290584 = 0.000000000 0.000000000 + x = -2.420614242 + 3.470290584 x = -2.420614242 + 3.470290584 Combine like terms: -2.420614242 + 3.470290584 = 1.049676342 x = 1.049676342 Simplifying x = 1.049676342Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.890904826, 1.049676342}
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