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Simplifying 3x2 + 35x + -5.7 = 0 Reorder the terms: -5.7 + 35x + 3x2 = 0 Solving -5.7 + 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'. -1.9 + 11.66666667x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + 11.66666667x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + 11.66666667x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + 11.66666667x + x2 = 0 + 1.9 11.66666667x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 11.66666667x + x2 = 1.9 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 = 1.9 + 34.02777780 Reorder the terms: 34.02777780 + 11.66666667x + x2 = 1.9 + 34.02777780 Combine like terms: 1.9 + 34.02777780 = 35.9277778 34.02777780 + 11.66666667x + x2 = 35.9277778 Factor a perfect square on the left side: (x + 5.833333335)(x + 5.833333335) = 35.9277778 Calculate the square root of the right side: 5.993978462 Break this problem into two subproblems by setting (x + 5.833333335) equal to 5.993978462 and -5.993978462.Subproblem 1
x + 5.833333335 = 5.993978462 Simplifying x + 5.833333335 = 5.993978462 Reorder the terms: 5.833333335 + x = 5.993978462 Solving 5.833333335 + x = 5.993978462 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 = 5.993978462 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = 5.993978462 + -5.833333335 x = 5.993978462 + -5.833333335 Combine like terms: 5.993978462 + -5.833333335 = 0.160645127 x = 0.160645127 Simplifying x = 0.160645127Subproblem 2
x + 5.833333335 = -5.993978462 Simplifying x + 5.833333335 = -5.993978462 Reorder the terms: 5.833333335 + x = -5.993978462 Solving 5.833333335 + x = -5.993978462 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 = -5.993978462 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = -5.993978462 + -5.833333335 x = -5.993978462 + -5.833333335 Combine like terms: -5.993978462 + -5.833333335 = -11.827311797 x = -11.827311797 Simplifying x = -11.827311797Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.160645127, -11.827311797}
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