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Unformatted text preview: o complete the square. Again, this is one-half
the coefficient of x, squared.
ç ÷= 2
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
x + x+ 2 = 2 4a
2 2 b ö b 2 - 4ac
çx+ ÷ =
Now we can use the square root property on this. x+ b
b 2 - 4ac
4a 2 Solve for x and we’ll also simplify the square root a little. x=- b
b 2 - 4ac
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
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]
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- Spring '12