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Simplifying 3x2 + -35x = 54 Reorder the terms: -35x + 3x2 = 54 Solving -35x + 3x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -35x + 3x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -35x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18 + -11.66666667x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -11.66666667x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -11.66666667x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -11.66666667x + x2 = 0 + 18 -11.66666667x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -11.66666667x + x2 = 18 The x term is -11.66666667x. Take half its coefficient (-5.833333335). Square it (34.02777780) and add it to both sides. Add '34.02777780' to each side of the equation. -11.66666667x + 34.02777780 + x2 = 18 + 34.02777780 Reorder the terms: 34.02777780 + -11.66666667x + x2 = 18 + 34.02777780 Combine like terms: 18 + 34.02777780 = 52.0277778 34.02777780 + -11.66666667x + x2 = 52.0277778 Factor a perfect square on the left side: (x + -5.833333335)(x + -5.833333335) = 52.0277778 Calculate the square root of the right side: 7.213028338 Break this problem into two subproblems by setting (x + -5.833333335) equal to 7.213028338 and -7.213028338.Subproblem 1
x + -5.833333335 = 7.213028338 Simplifying x + -5.833333335 = 7.213028338 Reorder the terms: -5.833333335 + x = 7.213028338 Solving -5.833333335 + x = 7.213028338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = 7.213028338 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = 7.213028338 + 5.833333335 x = 7.213028338 + 5.833333335 Combine like terms: 7.213028338 + 5.833333335 = 13.046361673 x = 13.046361673 Simplifying x = 13.046361673Subproblem 2
x + -5.833333335 = -7.213028338 Simplifying x + -5.833333335 = -7.213028338 Reorder the terms: -5.833333335 + x = -7.213028338 Solving -5.833333335 + x = -7.213028338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.833333335' to each side of the equation. -5.833333335 + 5.833333335 + x = -7.213028338 + 5.833333335 Combine like terms: -5.833333335 + 5.833333335 = 0.000000000 0.000000000 + x = -7.213028338 + 5.833333335 x = -7.213028338 + 5.833333335 Combine like terms: -7.213028338 + 5.833333335 = -1.379695003 x = -1.379695003 Simplifying x = -1.379695003Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.046361673, -1.379695003}
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