Question

Solve $4n^2-24n-56=8$by completing the square.

Short answer

The required solution is $n=-2,n=8$

Step-by-step solution

Given information

The equation given is$4n^2-24n-56=8$

Simplifying the expression

Dividing the equation by 4:

$n^2-6n-14=2$

Adding 14 on both sides:

$n^2-6n=16$

Adding ${\left(\frac{1}{2}*6\right)}^2=9$on both sides:

$n^2-6n+9=25$

Making whole square:

${(n-3)}^2=25$

Solving the equation:

$n=-2,n=8$