Question

Solve the equation by completing square method.

$2n^2+4n-26=0$

Short answer

The solutions are$n=-1\pm \sqrt{14}$.

Step-by-step solution

Given Information.

The Given equation is $2n^2+4n-26=0$.

Factor out the greatest common factor and divide both sides to isolate the trinomial. 

The GCF is $2$.

Divide both sides by $2$.

$$\begin{gathered} \frac{1}{2}(2n^2+4n-26)=0 \\ {n}^2+2n-13=0 \end{gathered}$$

Isolate the binomial term.

$n^2+2n=13$

Add role="math" localid="1648967730085" ${\left(\frac{1}{2}\times 2\right)}^2$to both sides.

$n^2+2n+1=13+1$

$n^2+2n+1=14$

Factor the perfect square trinomial as a binomial square.   

$(n+1{)}^2=14$

Use the square root property.

$n+1=\pm \sqrt{14}$

$n=-1\pm \sqrt{14}$

Rewrite to show two solutions.

$n=-1+\sqrt{14},n=-1-\sqrt{14}$.