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Simplifying -3x2 + -5x + 1082 = 0 Reorder the terms: 1082 + -5x + -3x2 = 0 Solving 1082 + -5x + -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'. -360.6666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '360.6666667' to each side of the equation. -360.6666667 + 1.666666667x + 360.6666667 + x2 = 0 + 360.6666667 Reorder the terms: -360.6666667 + 360.6666667 + 1.666666667x + x2 = 0 + 360.6666667 Combine like terms: -360.6666667 + 360.6666667 = 0.0000000 0.0000000 + 1.666666667x + x2 = 0 + 360.6666667 1.666666667x + x2 = 0 + 360.6666667 Combine like terms: 0 + 360.6666667 = 360.6666667 1.666666667x + x2 = 360.6666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 360.6666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 360.6666667 + 0.6944444447 Combine like terms: 360.6666667 + 0.6944444447 = 361.3611111447 0.6944444447 + 1.666666667x + x2 = 361.3611111447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 361.3611111447 Calculate the square root of the right side: 19.00950055 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 19.00950055 and -19.00950055.Subproblem 1
x + 0.8333333335 = 19.00950055 Simplifying x + 0.8333333335 = 19.00950055 Reorder the terms: 0.8333333335 + x = 19.00950055 Solving 0.8333333335 + x = 19.00950055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 19.00950055 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 19.00950055 + -0.8333333335 x = 19.00950055 + -0.8333333335 Combine like terms: 19.00950055 + -0.8333333335 = 18.1761672165 x = 18.1761672165 Simplifying x = 18.1761672165Subproblem 2
x + 0.8333333335 = -19.00950055 Simplifying x + 0.8333333335 = -19.00950055 Reorder the terms: 0.8333333335 + x = -19.00950055 Solving 0.8333333335 + x = -19.00950055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -19.00950055 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -19.00950055 + -0.8333333335 x = -19.00950055 + -0.8333333335 Combine like terms: -19.00950055 + -0.8333333335 = -19.8428338835 x = -19.8428338835 Simplifying x = -19.8428338835Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.1761672165, -19.8428338835}
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