# SOLUTION: how do you complete a square on this problem? 1/2x^2+1/3x-6=4

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 Click here to see ALL problems on Linear Algebra Question 23173: how do you complete a square on this problem? 1/2x^2+1/3x-6=4 Answer by AnlytcPhil(1278)   (Show Source): You can put this solution on YOUR website!```1/2x2 + 1/3x - 6 = 4 1. Divide through by the coefficient of x2 This is 1/2. To divide by 1/2 is to multiply through by 2 2(1/2x2) + 2(1/3x) - 2(6) = 2(4) x2 + 2/3x - 12 = 8 2. Get rid of the constant term on the left by adding its opposite to both sides: x2 + 2/3x = 8 + 12 x2 + 2/3x = 20 3. Find the square-completing number by (a) multiplying the coefficient of x by 1/2 (2/3)·(1/2) = 1/3 (b) squaring this result (1/3)2 = 1/9 4. Add the square-completing number to both sides x2 + 2/3x + 1/9 = 20 + 1/9 5. Factor the left side, and if everything is done right, it will factor into two equal factors, which is a perfect square: (x + 1/3)(x + 1/3) = 20 + 1/9 (x + 1/3)2 = 20 6. Combine the terms on the right (x + 1/3)2 = 180/9 + 1/9 (x + 1/3)2 = 181/9 6. Take the square roots of both sides, remembering to put ± on the right: _____ x + 1/3 = ±V181/9 5. Solve for x: _____ x = =1/3 ± Ö181/9 6. Simplify the radical: The numerator, 181, is a prime number, so we leave it under the radical. We take the square root of the denominator, 9, and get 3 ___ x = -1/3 ± Ö181/3 If you like you may write this as a single fraction with denomninator 3 ___ x = (-1 ± Ö181)/3 Edwin AnlytcPhil@aol.com```