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Simplifying 3.51x2 + -10.07x + 3.04 = 0 Reorder the terms: 3.04 + -10.07x + 3.51x2 = 0 Solving 3.04 + -10.07x + 3.51x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.51 the coefficient of the squared term: Divide each side by '3.51'. 0.8660968661 + -2.868945869x + x2 = 0 Move the constant term to the right: Add '-0.8660968661' to each side of the equation. 0.8660968661 + -2.868945869x + -0.8660968661 + x2 = 0 + -0.8660968661 Reorder the terms: 0.8660968661 + -0.8660968661 + -2.868945869x + x2 = 0 + -0.8660968661 Combine like terms: 0.8660968661 + -0.8660968661 = 0.0000000000 0.0000000000 + -2.868945869x + x2 = 0 + -0.8660968661 -2.868945869x + x2 = 0 + -0.8660968661 Combine like terms: 0 + -0.8660968661 = -0.8660968661 -2.868945869x + x2 = -0.8660968661 The x term is -2.868945869x. Take half its coefficient (-1.434472935). Square it (2.057712601) and add it to both sides. Add '2.057712601' to each side of the equation. -2.868945869x + 2.057712601 + x2 = -0.8660968661 + 2.057712601 Reorder the terms: 2.057712601 + -2.868945869x + x2 = -0.8660968661 + 2.057712601 Combine like terms: -0.8660968661 + 2.057712601 = 1.1916157349 2.057712601 + -2.868945869x + x2 = 1.1916157349 Factor a perfect square on the left side: (x + -1.434472935)(x + -1.434472935) = 1.1916157349 Calculate the square root of the right side: 1.091611531 Break this problem into two subproblems by setting (x + -1.434472935) equal to 1.091611531 and -1.091611531.Subproblem 1
x + -1.434472935 = 1.091611531 Simplifying x + -1.434472935 = 1.091611531 Reorder the terms: -1.434472935 + x = 1.091611531 Solving -1.434472935 + x = 1.091611531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.434472935' to each side of the equation. -1.434472935 + 1.434472935 + x = 1.091611531 + 1.434472935 Combine like terms: -1.434472935 + 1.434472935 = 0.000000000 0.000000000 + x = 1.091611531 + 1.434472935 x = 1.091611531 + 1.434472935 Combine like terms: 1.091611531 + 1.434472935 = 2.526084466 x = 2.526084466 Simplifying x = 2.526084466Subproblem 2
x + -1.434472935 = -1.091611531 Simplifying x + -1.434472935 = -1.091611531 Reorder the terms: -1.434472935 + x = -1.091611531 Solving -1.434472935 + x = -1.091611531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.434472935' to each side of the equation. -1.434472935 + 1.434472935 + x = -1.091611531 + 1.434472935 Combine like terms: -1.434472935 + 1.434472935 = 0.000000000 0.000000000 + x = -1.091611531 + 1.434472935 x = -1.091611531 + 1.434472935 Combine like terms: -1.091611531 + 1.434472935 = 0.342861404 x = 0.342861404 Simplifying x = 0.342861404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.526084466, 0.342861404}
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