Question

Question Solve 5a^2- 14a = -280 by completing the square. If there are multiple answers, list them separated by a comma (e.g. 1,2). If there is no real solution, enter Ø.

Answer 1

The equation is given as ;

`5a^2-14a=-280`

Divide both terms by 5 as;

`(5a^2)/(5)-(14a)/(5)=-(280)/(5)`

This will give the following;

`a^2-(14)/(5)a=\text{ -56}`

Find { b/2}^2 and add it on both sides of the equation where b is the second term in the equation.

{-14/5 / 2 }^2 = {-14/5 * 1/2 }^2 = {-14/10}^2 = {-7/5}^2 = 49/25

Add this on both sides of the equation as;

`a^2-(14)/(5)a+(49)/(25)=-56+(49)/(25)`

Factorize as ;

`(a-(7)/(5))^2=-54.04`

From the above, you notice, a square-root of a negative number will not result to real solutions for a, thus; the equation has no real solution.

Answer:

No real solution