how do i solve x2-26x+48

Question

how do i solve x2-26x+48

Answer 1

x^2-26x+48 is in the form ax^2+bx+c

a=1, b=-26 and c=48

because b is even, c must be factored into the product of two even numbers, NOT an even times an odd

therefore you cannot use 1*48 and  3*16

you can use 2*24, 4*12 or 6*8

looking at the products, which two numbers add or subtract to make 26 ? (disregarding signs for the moment)

2 and 24 add to make 26

48 is positive and 26 is negative so you use -2 and -24

(-2)(-24)=48 and -2+(-24)=-26

the answer is (x-2)(x-24)

if the problem is x^2-26x+48=0 then we have (x-2)(x-24)=0

x-2=0 and x-24=0

therefore x=2 and x=24

check by substituting the numbers 2 and 24, one at a time, into the original equation

2^2-26*2+48=0

4-52+48=0

24^2-26*24+48=0

576-624+48=0

Answer 2

The first thing I do is look at the last number, 48, and the number in front of the "x" variable, -24, and see if there are numbers that when multiplied together equals 48 and when added together equals -26. The numbers that satisfy both scenarios are -24 and -2. Putting these into the the form  (x-24)(x-2)=0 and performing F(first)O(outside)I(inside)L(last), or FOIL, you will get the original equation of x² -26x + 48=0.

Therefore, the solutions to the problem are

                                                               x=2 and x=24

 

 

Answer 3

I am assuming that in the equation you wrote x2 which is x raised to the power 2 which I would write as x^2. If that is what you mean then to solve this equation you need to factor and set equal to 0 and solve for x by setting each of the factors to 0.

 

x^2 - 26x + 48 factors into (x+a)(x+b) where ab=48 and a + b = -26

 

-24 x -2 = 48

-24 + -2 + -26

 

so we have (x + (-24))(x+(-2)) = (x - 24) (x - 2) = 0

 

x - 24 = 0 , x=24

x - 2 = 0,    x=2

 

You can check those two solutions by plugging back in

 

24^2 - 26x24 +48 = 0 that is correct

2^2 - 26x2 + 48 = 0 that is correct

 

You can also use the quadratic formula x = -b +/- (sqrt(b^2 - 4ac)/2a

 

equation above ax^2+bx+c where a=1, b=-26, c=48