4x^2-11x=3 Best answer")

Can you help me solve this and tell me how the middle term applies?

4x^2 - 11x = 3
4x^2 - 11x - 3 = 0

To factor: 4 * -3 = -12
-12 * 1 = -12 and -12 + 1 = -11, so replace -11x with -12x + x

4x^2 - 12x + x - 3 = 0
4x (x - 3) + 1 (x - 3) = 0
(x - 3) (4x + 1) = 0

x = 3, x = -1/4

4x² - 11x = 3

Subtract both sides by 3:

4x² - 11x - 3 = 0

Use factoring decomposition:

4x² - 12x + x - 3 = 0 . . . Split -11x into two terms that yield the product of -12 and sum of -11.
4x(x - 3) + 1(x - 3) = 0 . .Factor like terms
(4x + 1)(x - 3) = 0 . . . . .Group the common factors of x - 3 and collect the terms.

Finally, by zero-product property:

4x + 1 = 0 and x - 3 = 0
x = {-¼, 3}

I hope this helps!

4x^2 - 11x = 3
4x^2 - 11x - 3 = 0

At this point, you should look to determine whether it's factorable. Note that 4 * 3 = 12, and 1 * 1 = 1, and 12 - 1 = 11, so the coefficients of x in the two terms will be 4 and 1, and the constant terms will be 1 and 3 respectively. Set the signs correctly to get -11, which means negative three and positive 1 for the constant terms.

4x^2 - 11x - 3 = 0
(4x + 1)(x - 3) = 0
4x + 1 = 0 or x - 3 = 0
4x = -1 or x = 3
x = -1/4 or x = 3

4x^2-11x=3 Subtract 3
4x^2-11x-3=0 Factor
4x²-12x+x-3=0 Split -11x into two terms that equals the product of -12 and sum of -11.
4x(x-3)+1(x-3)=0 Group like terms
(4x+1)(x-3)=0 Set up =0 (when you foil, it gives you the first equation)
4x+1=0 x-3=0 Solve
4x=-1
x=-1/4 and x=3

You're Welcome!

first 4x^2 - 11x - 3 = 0

this is a quadratic polynomial
u need to know : ax^n + bx + c
if a + b + c = 0
then x=1 and x=c/a

if a - b + c = 0
then x=-1 and x=-c/a

so in this case none of the rules are applied; so u need to factorize
:P

4 x ² - 11x - 3 = 0
( 4x + 1 ) ( x - 3 ) = 0
x = - 1/4 , x = 3

4x² - 11x - 3 = 0

4x² - 12x + x - 3 = 0

4x(x - 3) + (x - 3) = 0

(4x + 1)(x - 3) = 0

x = -1/4 and 3

16x-11x=3
5x=3