At that point we can do some canceling x 2 16 2 2 2

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Unformatted text preview: o complete the square. Again, this is one-half the coefficient of x, squared. 2 b2 æbö ç ÷= 2 4a è 2a ø Now, add this to both sides, complete the square and get common denominators on the right side to simplify things up a little. b b2 b2 c x + x+ 2 = 2 4a 4a a a 2 2 b ö b 2 - 4ac æ çx+ ÷ = 2a ø 4a 2 è Now we can use the square root property on this. x+ b b 2 - 4ac =± 2a 4a 2 Solve for x and we’ll also simplify the square root a little. x=- b b 2 - 4ac ± 2a 2a As a last step we will notice that we’ve got common denominators on the two terms and so we’ll add them up. Doing this gives, -b ± b 2 - 4ac x= 2a So, summarizing up, provided that we start off in standard form, ax 2 + bx + c = 0 and that’s very important, then the solution to any quadratic equation is, x= -b ± b 2 - 4ac 2a Let’s work a couple of examples. Example 3 Use the quadratic formula to solve each of the following equations. (a) x 2 + 2 x = 7 [Solution] (b) 3q 2 + 11 = 5q [Solution] (c) 7t 2 = 6 - 19t [Solution] 3 1 (d...
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