This is a free lesson from our course in Algebra I
In this section, you'll learn another approach to using the quadratic formula. If the left hand side of a given equation
ax^{2} + bx + c = 0 cannot be factorized easily into the
product of a pair of binomials, then it can be solved by using the quadratic
formula x = {b
(b^{2}
 4ac)}/2a and it'll have two roots. For example, if you use the quadratic formula
to solve equation x^{2} + 2x + 7, you get two roots x
= 1
22. There are some quadratics (most of them, actually) that you can't solve by factoring. But the Quadratic Formula will always work, whether the quadratic was factorable or not.(More text below video...)
(Continued from above) For example, use the Quadratic Formula to solve x^{2} – 4x – 8 = 0.
Looking at the coefficients, you see that a = 1, b = –4, and c = –8. Plug them into the Formula, and simplify. x = (4) ± (4)2 – 4(1)(8) / 2(1)
= 4 ± (16 + 32) / 2
= 4 ± 48 / 2
= 4 ± 43 / 2
= 2 ± 23
= 2(1 ± 3)
Then the solution is x = 2(1 ± 3).
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