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Simplifying (3x2) + 35x + -4.5 = 0 Reorder the terms: -4.5 + 35x + (3x2) = 0 Solving -4.5 + 35x + (3x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.5 + 11.66666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 11.66666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 11.66666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 11.66666667x + x2 = 0 + 1.5 11.66666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 11.66666667x + x2 = 1.5 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 = 1.5 + 34.02777780 Reorder the terms: 34.02777780 + 11.66666667x + x2 = 1.5 + 34.02777780 Combine like terms: 1.5 + 34.02777780 = 35.5277778 34.02777780 + 11.66666667x + x2 = 35.5277778 Factor a perfect square on the left side: ((x) + 5.833333335)((x) + 5.833333335) = 35.5277778 Calculate the square root of the right side: 5.960518249 Break this problem into two subproblems by setting ((x) + 5.833333335) equal to 5.960518249 and -5.960518249.Subproblem 1
(x) + 5.833333335 = 5.960518249 Simplifying (x) + 5.833333335 = 5.960518249 x + 5.833333335 = 5.960518249 Reorder the terms: 5.833333335 + x = 5.960518249 Solving 5.833333335 + x = 5.960518249 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 = 5.960518249 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = 5.960518249 + -5.833333335 x = 5.960518249 + -5.833333335 Combine like terms: 5.960518249 + -5.833333335 = 0.127184914 x = 0.127184914 Simplifying x = 0.127184914Subproblem 2
(x) + 5.833333335 = -5.960518249 Simplifying (x) + 5.833333335 = -5.960518249 x + 5.833333335 = -5.960518249 Reorder the terms: 5.833333335 + x = -5.960518249 Solving 5.833333335 + x = -5.960518249 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 = -5.960518249 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = -5.960518249 + -5.833333335 x = -5.960518249 + -5.833333335 Combine like terms: -5.960518249 + -5.833333335 = -11.793851584 x = -11.793851584 Simplifying x = -11.793851584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.127184914, -11.793851584}
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