Solve the equation 2x^2 - 18x + 36 = 0

6 Answers | Add Yours

knowledgeseeker1's profile pic

knowledgeseeker1 | (Level 1) Adjunct Educator

Posted on

2x^2 - 18x + 36 = 0

or x^2 - 9x + 18 = 0

any quadratic equation can be expressed as 

x^2 - (sum of roots) x + (product of roots) = 0

where sum of roots and product of roots are decimal values (for real roots).

Here sum of roots is 9 and product of roots is 18. Let's say the roots are a and b.

So 

a+b=9 and a*b = 18

which gives roots as 3 and 6.

so the values of x can be 3 or 6.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The solution of a quadratic equation of the form ax^2 + bx + c = 0 is `(-b+-sqrt(b^2 - 4ac))/(2a)`

2x^2 - 18x + 36 = 0

=> x^2 - 9x + 18 = 0

Substituting the value of a, b and c in the formula given earlier, the roots of the equation are:

`(9 +- sqrt(81 - 4*18))/2`

= `(9 +- sqrt(81 - 72))/2`

= `(9 +- sqrt(9))/2`

= `(9 +- 3)/2`

The roots of the equation are 3 and 6.

sid-sarfraz's profile pic

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

Posted on

`2x^2 - 18x + 36 = 0`

``

``

SOLUTION:-

WE will use the quadratic formula in order to solve this problem, which is;

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

Where;

a = 2

b = -18

c = 36

Insert values in the formula;

x = {-(-18) +-sqrt((-18)^2 -4(2)(36))}/2(2)

x = {18 +-sqrt(324 - 288)}/4

x = {18 +-sqrt(36)} /4

Since the square root of 36 is 6 therefore;

x = (18 +- 6)/4

Now the two solutions that we can get from this are:

x = (18 + 6)/4             ,             x = (18 - 6)/4

x = 24/4                     ,             x = 12/4

x= 6                           ,             x = 3

Hence the solution set is (6,3)

Hence Solved!

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

2x^2 - 18x + 36 = 0

The above equation is in the form of a quadratic equation therefore we can solve it with the help of a quadratic formula:

Where a=2

          b=-18

          c=36

x=[18+sqrt{(-18)^2-4(2)(36)}]/2(2)     x=[18-sqrt{(-18)^2-4(2)(36)}]/2(2)

  =[18+sqrt{324-288}]/4                       =[18-sqrt{324-288}]/4

  =[18+6]/4                                           =[18-6]/4

  =24/4                                                 =12/4

  =6                                                      =3

Solution Set= (6,3)

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

2x^2 - 18x + 36 = 0

This equation is in the form of quadratic equation i.e 

Where, a=2

           b=-18

           c=36

Then we input these values in the quadratic formula i.e 

=[-(-18)+sqrt{(-18)^2-4(2)(36)}]/4        =[-(-18)-sqrt{(-18)^2-4(2)(36)}]/4 

=[18+sqrt{324-288}]/4                          =[18-sqrt{324-288}]/4

={18+sqrt(36)}/4                                   ={18-sqrt(36)}/4

=(18+6)/4                                              =(18-6)/4

=24/4                                                    =12/4

=6                                                         =3

Solution Set= (6,3)

rachellopez's profile pic

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

Posted on

Since this equation doesn't easily factor, I would go straight to the quadratic formula. The quadratic formula is `(-b+-sqrt(b^2-4ac))/(2a)`.

All you need to do is substitute in the numbers. For the equation you have, 2x^2-18x+36, your a=2, b=-18, and c=36.

`(-(-18)+-sqrt(18^2-4(2)(36)))/(2(2))`

`(18+-sqrt(36))/(4)`

`(18+-6)/(4)`

You can easily solve for both 18+6 divided by 4 and 18-6 divided by 4 with a calculator. You end up with solutions of x=6 and x=3.

We’ve answered 318,928 questions. We can answer yours, too.

Ask a question