Question

Solve the equation by completing square method.$\left(u+8\right)\left(u+4\right)=14$

Short answer

The solution are$u=\pm 3\sqrt{2}-6$

Step-by-step solution

Given Information.   

The Given equation is $\left(u+8\right)\left(u+4\right)=14$

Simplify the expression    

$$\begin{gathered} u^2+8u+4u+32=14 \\ {u}^2+12u+32=14 \end{gathered}$$

Isolate the variable terms on one side and the constant terms on the other.The variable terms are on the left side.

$u^2+12u=-18$

The coefficient of $u$is $12$

So ,$b=12$

Find 12b2and add to the both sides of equation.

$$\begin{gathered} ={\left(\frac{1}{2}\left(12\right)\right)}^2 \\ ={\left(6\right)}^2 \\ =36 \end{gathered}$$

Add $81$both side of equation

$u^2+12u+36=-18+36$

$u^2+12u+36=18$

Factor the perfect square trinomial as a binomial square    

${\left(u+6\right)}^2=18$

Use square root property

$$\begin{gathered} \left(u+6\right)=\pm \sqrt{18} \\ \left(u+6\right)=\pm 3\sqrt{2} \\ u=\pm 3\sqrt{2}-6 \\ u=3\sqrt{2}-6,-3\sqrt{2}-6 \end{gathered}$$