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Simplifying -2x2 + 267x + -682 = 0 Reorder the terms: -682 + 267x + -2x2 = 0 Solving -682 + 267x + -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'. 341 + -133.5x + x2 = 0 Move the constant term to the right: Add '-341' to each side of the equation. 341 + -133.5x + -341 + x2 = 0 + -341 Reorder the terms: 341 + -341 + -133.5x + x2 = 0 + -341 Combine like terms: 341 + -341 = 0 0 + -133.5x + x2 = 0 + -341 -133.5x + x2 = 0 + -341 Combine like terms: 0 + -341 = -341 -133.5x + x2 = -341 The x term is -133.5x. Take half its coefficient (-66.75). Square it (4455.5625) and add it to both sides. Add '4455.5625' to each side of the equation. -133.5x + 4455.5625 + x2 = -341 + 4455.5625 Reorder the terms: 4455.5625 + -133.5x + x2 = -341 + 4455.5625 Combine like terms: -341 + 4455.5625 = 4114.5625 4455.5625 + -133.5x + x2 = 4114.5625 Factor a perfect square on the left side: (x + -66.75)(x + -66.75) = 4114.5625 Calculate the square root of the right side: 64.1448556 Break this problem into two subproblems by setting (x + -66.75) equal to 64.1448556 and -64.1448556.Subproblem 1
x + -66.75 = 64.1448556 Simplifying x + -66.75 = 64.1448556 Reorder the terms: -66.75 + x = 64.1448556 Solving -66.75 + x = 64.1448556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.75' to each side of the equation. -66.75 + 66.75 + x = 64.1448556 + 66.75 Combine like terms: -66.75 + 66.75 = 0.00 0.00 + x = 64.1448556 + 66.75 x = 64.1448556 + 66.75 Combine like terms: 64.1448556 + 66.75 = 130.8948556 x = 130.8948556 Simplifying x = 130.8948556Subproblem 2
x + -66.75 = -64.1448556 Simplifying x + -66.75 = -64.1448556 Reorder the terms: -66.75 + x = -64.1448556 Solving -66.75 + x = -64.1448556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.75' to each side of the equation. -66.75 + 66.75 + x = -64.1448556 + 66.75 Combine like terms: -66.75 + 66.75 = 0.00 0.00 + x = -64.1448556 + 66.75 x = -64.1448556 + 66.75 Combine like terms: -64.1448556 + 66.75 = 2.6051444 x = 2.6051444 Simplifying x = 2.6051444Solution
The solution to the problem is based on the solutions from the subproblems. x = {130.8948556, 2.6051444}
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