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Simplifying 7x2 + -266x + 2518 = 0 Reorder the terms: 2518 + -266x + 7x2 = 0 Solving 2518 + -266x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 359.7142857 + -38x + x2 = 0 Move the constant term to the right: Add '-359.7142857' to each side of the equation. 359.7142857 + -38x + -359.7142857 + x2 = 0 + -359.7142857 Reorder the terms: 359.7142857 + -359.7142857 + -38x + x2 = 0 + -359.7142857 Combine like terms: 359.7142857 + -359.7142857 = 0.0000000 0.0000000 + -38x + x2 = 0 + -359.7142857 -38x + x2 = 0 + -359.7142857 Combine like terms: 0 + -359.7142857 = -359.7142857 -38x + x2 = -359.7142857 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -359.7142857 + 361 Reorder the terms: 361 + -38x + x2 = -359.7142857 + 361 Combine like terms: -359.7142857 + 361 = 1.2857143 361 + -38x + x2 = 1.2857143 Factor a perfect square on the left side: (x + -19)(x + -19) = 1.2857143 Calculate the square root of the right side: 1.133893425 Break this problem into two subproblems by setting (x + -19) equal to 1.133893425 and -1.133893425.Subproblem 1
x + -19 = 1.133893425 Simplifying x + -19 = 1.133893425 Reorder the terms: -19 + x = 1.133893425 Solving -19 + x = 1.133893425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 1.133893425 + 19 Combine like terms: -19 + 19 = 0 0 + x = 1.133893425 + 19 x = 1.133893425 + 19 Combine like terms: 1.133893425 + 19 = 20.133893425 x = 20.133893425 Simplifying x = 20.133893425Subproblem 2
x + -19 = -1.133893425 Simplifying x + -19 = -1.133893425 Reorder the terms: -19 + x = -1.133893425 Solving -19 + x = -1.133893425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -1.133893425 + 19 Combine like terms: -19 + 19 = 0 0 + x = -1.133893425 + 19 x = -1.133893425 + 19 Combine like terms: -1.133893425 + 19 = 17.866106575 x = 17.866106575 Simplifying x = 17.866106575Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.133893425, 17.866106575}
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