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;

$\frac{5a^2}{5}-\frac{14a}{5}=-\frac{280}{5}$

This will give the following;

$a^2-\frac{14}{5}a=\text{ -56}$

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;

$a^2-\frac{14}{5}a+\frac{49}{25}=-56+\frac{49}{25}$

Factorize as ;

$(a-\frac{7}{5})^2=-54.04$

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