Answer:
x = 1 or -3/4
factoring is easier for me
Step-by-step explanation:
<u>Factoring</u>
We rewrite to ...
4x^2 -x -3 = 0
We want factors of (4)(-3) = -12 that have a sum of -1. They are -4 and 3. Then the factorization is ...
(4x -4)(4x +3)/4 = (x -1)(4x +3)
Solutions are values of x that make the factors zero: x = 1, x = -3/4.
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<u>Completing the square</u>
We start by factoring the leading coefficient from the left side:
4(x^2 -x/4) = 3
Now, we add the square of half the x-coefficient (inside parentheses):
4(x^2 -x/4 +1/64) = 3 + 4/64
4(x -1/8)^2 = 49/16 . . . . . . . . . write as squares
x -1/8 = ±√(49/64) = ±7/8
x = 1/8 ± 7/8
x = -3/4 or +1
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<u>Preference</u>
In this instance <em>I prefer factoring</em>, because it deals with whole numbers up until the end. It does not involve adding and subtracting fractions. On this page, it takes fewer steps.
If you're unfamiliar with math facts, such as the factors of 12, then the purely mechanical "completing the square" method may be preferable. It does not require anything other than finding half of a number and then squaring that.
