Can you solve this quadratic equation/find the value of x?

Question

11x² - 1056x + 25344 = 0
Please, show the working.

Answer 1

11x² - 1056x + 25344 = 0

I'm basically a lazy individual. i don't use a calculator much, and I REALLY dislike multiplying large numbers by hand
It would be really neat if 11 was a factor in all three numeric coefficients... right?
So I checked...
(1)(11) = 11
(96)(11) = 1056
(2304)(11) = 25344

So you now have
x² - 96x + 2304 = 0

This looks more manageable... right?
I wonder if 2304 is a perfect square....

Turns out that 2304 = 48²
And fortunately, 96 = 48 + 48

So the darn thing factors to (x - 48)²

BUT.,, you said Quadratic Formula.
The Quadratic Formula
x = {-(b) ±√[(b)² - 4(a)(c)]}/[2(a)]
Substituting
x = {-(-1056) ±√[(-1056)² - 4(11)(25344)]}/[2(11)]
x = {1056 ±√[1115136 - 1115136]}/22
x = {1056 ±√[0]}/22

x = 48

Answer 2

First of all let us keep 11 as common:

So, dividing the equation on both the sides with 11, we get:

x^2 - 96x + 2304 = 0

Now we have formula :

x= {-b +/- (root) delta}/2a
where
a= 1
b= -96
c= 2304

Take Delta = b^2 - 4ac

= (96)^2 - 4*1*2304

= 9216 - 9216

= 0

S0, whenever delta is zero, the quadratic equation has equal roots, so it will be only:

x= -b/2a
= -(-96)/2*1
= (96)/2
= 48.

Answer 3

11x^2 - 1056x + 25344 = 0
therefore
11(x^2 - 96x + 2304) = 0
thus the equation is now reduced to
x^2 - 96x +2304 = 0
therefore
x^2 - 2(48)x + (48)^2 = 0 ---------------------------(1)
since square of 48 is 2304
the expression 1 is of the type
(a - b)^2 = a^2 - 2ab + b^2
therefore
our expression becomes
(x - 48)^2 = 0
therefore
x - 48 = 0
and x = 48 is the only root of the equation.

Answer 4

11x^2 -1056x + 25344 = 0
divide by 11 and get: x^2 - 96x + 2304 = 0
also x^2 - 96x + 2304 = ( x - 48)^2 = 0

There is a unique solution x = 48.

Answer 5

48 is the correct answer using the quadratic equation.
x= (-(-1056)+-√-1056²-4(11 x 25,344))/2*11
x=(1056+-√1,115,136-1,115,136)/22
for some reason the /22 on the above line is showing up as 3 dots (...) i've tried to fix it several times
x=(1056+-0)/22
x=48

Answer 6

11x2 -1056x + 25344 = 0 /11
x2 -96x + 2304 = take the square of 2304
x2 -96x +2304 = (x - 48) (x -48)

not as nice as other methods perhaps when factoring I was taught to rationalize the signs. if binomial - then must me neg to make the number last be a positive ans so on.......

Answer 7

11x^2-1056x+25344=0
divide both sides by 11;
x^2-96x+2304=0
x^2-2*48*x+48^2=0
(x-48)^2=0
x=48 ANS.

Answer 8

x = 48
Using quadratic formula,
x = 1056/22 = 48

Answer 9

11x^2-1056+25344=0
11(x^2-96x+2304)=0
11(x-48)^2=0

value of x = 48

Answer 10

4x^2 + 16x + 15 =0 (2x+3)(2x+5) =0 2x+3 =0 2x=-3 x=-3/2 2x+5 =0 2x=-5 x=-5/2 6x^2 + 29x - 5=0 (6x-a million)(x+5) =0 6x-a million=0 6x=a million x=a million/6 x+5=0 x=-5 4x^2 - 25x + 25=0 (4x-5)(x-5)=0 4x-5=0 4x=5 x=5/4 x-5=0 x=5