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Simplifying 6x2 + -29x + -49 = 0 Reorder the terms: -49 + -29x + 6x2 = 0 Solving -49 + -29x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -8.166666667 + -4.833333333x + x2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + -4.833333333x + 8.166666667 + x2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + -4.833333333x + x2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + -4.833333333x + x2 = 0 + 8.166666667 -4.833333333x + x2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 -4.833333333x + x2 = 8.166666667 The x term is -4.833333333x. Take half its coefficient (-2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. -4.833333333x + 5.840277779 + x2 = 8.166666667 + 5.840277779 Reorder the terms: 5.840277779 + -4.833333333x + x2 = 8.166666667 + 5.840277779 Combine like terms: 8.166666667 + 5.840277779 = 14.006944446 5.840277779 + -4.833333333x + x2 = 14.006944446 Factor a perfect square on the left side: (x + -2.416666667)(x + -2.416666667) = 14.006944446 Calculate the square root of the right side: 3.742585262 Break this problem into two subproblems by setting (x + -2.416666667) equal to 3.742585262 and -3.742585262.Subproblem 1
x + -2.416666667 = 3.742585262 Simplifying x + -2.416666667 = 3.742585262 Reorder the terms: -2.416666667 + x = 3.742585262 Solving -2.416666667 + x = 3.742585262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = 3.742585262 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = 3.742585262 + 2.416666667 x = 3.742585262 + 2.416666667 Combine like terms: 3.742585262 + 2.416666667 = 6.159251929 x = 6.159251929 Simplifying x = 6.159251929Subproblem 2
x + -2.416666667 = -3.742585262 Simplifying x + -2.416666667 = -3.742585262 Reorder the terms: -2.416666667 + x = -3.742585262 Solving -2.416666667 + x = -3.742585262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.416666667' to each side of the equation. -2.416666667 + 2.416666667 + x = -3.742585262 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + x = -3.742585262 + 2.416666667 x = -3.742585262 + 2.416666667 Combine like terms: -3.742585262 + 2.416666667 = -1.325918595 x = -1.325918595 Simplifying x = -1.325918595Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.159251929, -1.325918595}
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