24x^2-22x+3
are you factoring?
To factor, find two factors of the first and third terms that, when multiplied, will add to find the value of the center term.
(3,1 or -3,-1) and (4,6 or 2,12 or 3,8)
24x^2-22x+3 = (6x-1)(4x-3)
The expression you provided, 24x^2 - 22x + 3, is a quadratic expression. To simplify or factorize it, you can follow these steps:
Step 1: Check if the expression can be factored using the factorization method. In this case, the expression is a quadratic trinomial, as it has a degree of 2.
Step 2: Look for two numbers that can be multiplied to give you the product of the coefficient of x^2 (24) and the constant term (3), which is 72. The numbers should also add up to give you the coefficient of x (-22). In this case, there are no such numbers.
Since no simple factorization can be found, you can use the quadratic formula to find the roots or solutions of the quadratic equation. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the quadratic expression to a standard quadratic equation, ax^2 + bx + c, we can see that:
a = 24
b = -22
c = 3
Substituting the values into the quadratic formula, we get:
x = (-(-22) ± √((-22)^2 - 4(24)(3))) / (2(24))
Simplifying:
x = (22 ± √(484 - 288)) / 48
x = (22 ± √196) / 48
The square root of 196 is 14:
x = (22 ± 14) / 48
Now we can find the two possible solutions:
x = (22 + 14) / 48 = 36 / 48 = 3/4
x = (22 - 14) / 48 = 8 / 48 = 1/6
So the solutions to the quadratic equation 24x^2 - 22x + 3 are x = 3/4 and x = 1/6.