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Simplifying 2x2 + -41x + 150 = 0 Reorder the terms: 150 + -41x + 2x2 = 0 Solving 150 + -41x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 75 + -20.5x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -20.5x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -20.5x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -20.5x + x2 = 0 + -75 -20.5x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -20.5x + x2 = -75 The x term is -20.5x. Take half its coefficient (-10.25). Square it (105.0625) and add it to both sides. Add '105.0625' to each side of the equation. -20.5x + 105.0625 + x2 = -75 + 105.0625 Reorder the terms: 105.0625 + -20.5x + x2 = -75 + 105.0625 Combine like terms: -75 + 105.0625 = 30.0625 105.0625 + -20.5x + x2 = 30.0625 Factor a perfect square on the left side: (x + -10.25)(x + -10.25) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (x + -10.25) equal to 5.48292805 and -5.48292805.Subproblem 1
x + -10.25 = 5.48292805 Simplifying x + -10.25 = 5.48292805 Reorder the terms: -10.25 + x = 5.48292805 Solving -10.25 + x = 5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = 5.48292805 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = 5.48292805 + 10.25 x = 5.48292805 + 10.25 Combine like terms: 5.48292805 + 10.25 = 15.73292805 x = 15.73292805 Simplifying x = 15.73292805Subproblem 2
x + -10.25 = -5.48292805 Simplifying x + -10.25 = -5.48292805 Reorder the terms: -10.25 + x = -5.48292805 Solving -10.25 + x = -5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.25' to each side of the equation. -10.25 + 10.25 + x = -5.48292805 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + x = -5.48292805 + 10.25 x = -5.48292805 + 10.25 Combine like terms: -5.48292805 + 10.25 = 4.76707195 x = 4.76707195 Simplifying x = 4.76707195Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.73292805, 4.76707195}
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