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Simplifying 3x2 + 35x + -75 = 0 Reorder the terms: -75 + 35x + 3x2 = 0 Solving -75 + 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'. -25 + 11.66666667x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 11.66666667x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 11.66666667x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 11.66666667x + x2 = 0 + 25 11.66666667x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 11.66666667x + x2 = 25 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 = 25 + 34.02777780 Reorder the terms: 34.02777780 + 11.66666667x + x2 = 25 + 34.02777780 Combine like terms: 25 + 34.02777780 = 59.0277778 34.02777780 + 11.66666667x + x2 = 59.0277778 Factor a perfect square on the left side: (x + 5.833333335)(x + 5.833333335) = 59.0277778 Calculate the square root of the right side: 7.682953716 Break this problem into two subproblems by setting (x + 5.833333335) equal to 7.682953716 and -7.682953716.Subproblem 1
x + 5.833333335 = 7.682953716 Simplifying x + 5.833333335 = 7.682953716 Reorder the terms: 5.833333335 + x = 7.682953716 Solving 5.833333335 + x = 7.682953716 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 = 7.682953716 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = 7.682953716 + -5.833333335 x = 7.682953716 + -5.833333335 Combine like terms: 7.682953716 + -5.833333335 = 1.849620381 x = 1.849620381 Simplifying x = 1.849620381Subproblem 2
x + 5.833333335 = -7.682953716 Simplifying x + 5.833333335 = -7.682953716 Reorder the terms: 5.833333335 + x = -7.682953716 Solving 5.833333335 + x = -7.682953716 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 = -7.682953716 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = -7.682953716 + -5.833333335 x = -7.682953716 + -5.833333335 Combine like terms: -7.682953716 + -5.833333335 = -13.516287051 x = -13.516287051 Simplifying x = -13.516287051Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.849620381, -13.516287051}
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