Find the real solutions, if any, of the given equation.
(3/4)x^2 - (1/4)x - (1/2) = 0
Let me see.
I can use the quadratic formula. In the formula, a = 3/4, b = -1/4 and c = -1/2.
Yes?
You could but it'll be a bit tedious, with all those fractions. It's much easier to get rid of the fractions by
multiplying the equation by its LCD, 4. This'll give you:
Now, you can use the quadratic equation formula, but this quadratic (as is obvious, MAYBE), can be factored by
using the "ac" method, which requires 2 factors that have a PRODUCT of - 6 (a * c = + 3 * - 2), and a SUM of - 1
(b, or the coefficient on "x"). These 2 FACTORS are - 3 and + 2.
We then get the following: 3x2 - x - 2 = 0
3x2 - 3x + 2x - 2 = 0 ----- Replacing - x with - 3x + 2x
3x2 - 3x + 2x - 2 = 0 ----- PAIRing binomials
3x(x - 1) + 2(x - 1) = 0
(3x + 2)(x - 1) = 0 ----- FACTORED form
3x + 2 = 0 | x - 1 = 0
3x = - 2 | x = 0 + 1
OR