Solve `x^2 + 24 = 11x` by using the quadratic formula. Identify a,b, and c. Identify the solution set.

5 Answers

lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on


To solve this using quadractic formula

`x= (-b+-sqrt(b^2-4ac))/(2a)`

the equation should be in the form `ax^2+bx+c=0` .

So, to have zero at the right side, subtract both sides by 11x.
`x^2 +24-11x = 11x -11x`

`x^2-11x + 24 = 0`

Base on that, the values of a, b and c are:

a=1, b=-11 and c=24

Now that their values are known, plug-in them to the quadratic formula.




Then, seperate the +/- sign in the numerator.



Therefore, the solution set for `x^2+4x=11x`   is  `{3,8}` .

sid-sarfraz's profile pic

sid-sarfraz | Student, Graduate | (Level 2) Salutatorian

Posted on


Solve `x^2+24=11x` by using the quadratic formula.

  • Identify a,b, and c.
  • Identify the solution set.


The quadratic formula for a equation is;


`Quadratic Equation :-`


The given equation;




a = 1

b = -11

c = 24

Insert the values of a , b and c in the quadratic equation;


` `

Now simplify:




The two values of x are as follows:-




Hence the solution set is:{8,3}

Hence Solved!

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

In order to solve this through quadratic formula, we need to change it to this equation format ax^2+bx+c=0


Quadratic formula

Where, a=1




x=[-(-11)-sqrt{(-11)^2-4(1)(24)}]/2(1)   ` `









x=8 Answer

x=3 Answer

ayl0124's profile pic

ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

Posted on

Look at the function:

`y = ax^2 + bx + c`

Change the form of your original equation.

`y = x^2 -11x + 24`

Your "a" would be 1, your "b" would be -11, and your "c" would be 24.

```x = (-b +- sqrt(b^2 + 4ac))/(2a)`

Plug in your a, b, and c values.

`x = (11 + sqrt(121+(4)(1)(24)))/((2)(1)) = 8`

`x = (11 - sqrt(121 + (4)(1)(24)))/((2)(1)) = 3` 

You can also factor the equation.

`y = (x-8)(x-3)`

Jyotsana's profile pic

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

Posted on


x=(-(-11)+square root (-11)^2-4(1)(24))/2(1)

x=(-(-11)-square root(-11)^2-4(1)(24))/2(1)

x=8  or x=3