Can you please write this statement into algebraic expression and simplify into quadratic equation.( Three time square the number and 2 times fifth the number all divide by the number plus 7 all...

 Can you please write this statement into algebraic expression and simplify into quadratic equation.

( Three time square the number and 2 times fifth the number all divide by the number plus 7 all added to 9 equals 0.

Asked on by genieee

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Let the number in the problem be represented by x.

Now three time square the number and 2 times fifth the number all divide by the number plus 7 all added to 9 equals 0

(3*x^2 + 2x/5)/(x + 7) + 9 = 0

=> (3*x^2 + 2x/5)/(x + 7)  = -9

=> (3*x^2 + 2x/5) = -9(x + 7)

=> 3x^2 + 2x/5 = -9x - 63

=> 15x^2 + 2x = -45x - 315

=> 15x^2 + 47x + 315 = 0

The quadratic equation we get is 15x^2 + 47x + 315 = 0

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let us assume that the number is x.

Then 3 times square x is 3x^2.

And we will add 2 times fifth x ==> 3x^2 + 2x/5 = 3x^2 +(2/5)x

==> All divide by (x+7)  ==> [(3x^2 + (2/5)x] / (x+7)

==> all added to 9 ==> [ 3x^2+ (2/5)x ] / (x+ 7)  + 9 = 0

==>  (3x^2 + 2x/5 ) / (x+7) + 9 = 0

We will simplify.

 

==> (15x^2 + 2x) / 5(x+7) + 9 = 0

==> 15x^2 + 2x = -45 (x+ 7)

 

==> 15x^2 + 2x = -45x - 315

==> 15x^2 + 47x + 315 = 0

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