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Simplifying -5.5x2 + 275x + -139 = 1906 Reorder the terms: -139 + 275x + -5.5x2 = 1906 Solving -139 + 275x + -5.5x2 = 1906 Solving for variable 'x'. Reorder the terms: -139 + -1906 + 275x + -5.5x2 = 1906 + -1906 Combine like terms: -139 + -1906 = -2045 -2045 + 275x + -5.5x2 = 1906 + -1906 Combine like terms: 1906 + -1906 = 0 -2045 + 275x + -5.5x2 = 0 Begin completing the square. Divide all terms by -5.5 the coefficient of the squared term: Divide each side by '-5.5'. 371.8181818 + -50x + x2 = 0 Move the constant term to the right: Add '-371.8181818' to each side of the equation. 371.8181818 + -50x + -371.8181818 + x2 = 0 + -371.8181818 Reorder the terms: 371.8181818 + -371.8181818 + -50x + x2 = 0 + -371.8181818 Combine like terms: 371.8181818 + -371.8181818 = 0.0000000 0.0000000 + -50x + x2 = 0 + -371.8181818 -50x + x2 = 0 + -371.8181818 Combine like terms: 0 + -371.8181818 = -371.8181818 -50x + x2 = -371.8181818 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -371.8181818 + 625 Reorder the terms: 625 + -50x + x2 = -371.8181818 + 625 Combine like terms: -371.8181818 + 625 = 253.1818182 625 + -50x + x2 = 253.1818182 Factor a perfect square on the left side: (x + -25)(x + -25) = 253.1818182 Calculate the square root of the right side: 15.9116881 Break this problem into two subproblems by setting (x + -25) equal to 15.9116881 and -15.9116881.Subproblem 1
x + -25 = 15.9116881 Simplifying x + -25 = 15.9116881 Reorder the terms: -25 + x = 15.9116881 Solving -25 + x = 15.9116881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 15.9116881 + 25 Combine like terms: -25 + 25 = 0 0 + x = 15.9116881 + 25 x = 15.9116881 + 25 Combine like terms: 15.9116881 + 25 = 40.9116881 x = 40.9116881 Simplifying x = 40.9116881Subproblem 2
x + -25 = -15.9116881 Simplifying x + -25 = -15.9116881 Reorder the terms: -25 + x = -15.9116881 Solving -25 + x = -15.9116881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -15.9116881 + 25 Combine like terms: -25 + 25 = 0 0 + x = -15.9116881 + 25 x = -15.9116881 + 25 Combine like terms: -15.9116881 + 25 = 9.0883119 x = 9.0883119 Simplifying x = 9.0883119Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.9116881, 9.0883119}
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