4x^2-8x=21
how do you work this out?
4x^2 - 8x = 21
4x^2 - 8x - 21 = 0
We have to factor the left side; this is where most
people simply give up.
Start by factoring the first term: (2x)(2x)
Now, we need factors of 21. Not many to choose from.
Either (21)(1) or (7)(3).
With a little experimenting, we find that
(2 * -7) + (2 * 3) gives us -8, which is the co-efficient of x
in our equation.
(2x - 7)(2x + 3) = 0
One of those factors has to be zero to give zero as the result
of our multiplication. Set each factor to zero and solve for x.
(2x - 7) = 0
2x = 7
x = 3.5
(2x + 3) = 0
2x = -3
x = -1.5
Graphing the equation shows us a parabola that crosses the
x-axis in two places. That's why we have two solutions.
Check them.
4x^2 - 8x = 21
4(3.5)^2 - 8(3.5) = 21
4(12.25) - 28 = 21
49 - 28 = 21
21 = 21 That's correct.
4x^2 - 8x = 21
4(-1.5)^2 - 8(-1.5) = 21
4(2.25) + 12 = 21
9 + 12 = 21
21 = 21 That's correct, too.
The answer is: x = 3.5, and x = -1.5