Question

Solve the equation by completing square method.

$w^2+8w=65$

Short answer

The solutions are$w=5,w=-13$

Step-by-step solution

Given Information.   

The Given equation is $w^2+8w=65$.

Isolate the variable terms on one side and the constant terms on the other. 

The variable terms are on the left side.

$w^2+8w=65$

The coefficient of $w$is $8$.

So,$b=8$.

Find 12b2 and add to the both sides of equation. 

$$\begin{gathered} ={\left(\frac{1}{2}\left(8\right)\right)}^2 \\ ={\left(4\right)}^2=16 \end{gathered}$$

Add $16$both sides.

$$\begin{gathered} w^2+8w+16=65+16 \\ {w}^2+8w+16=81 \end{gathered}$$

Factor the perfect square trinomial as a binomial square. 

$(w+4{)}^2=81$

Use the square root property.

$$\begin{gathered} w+4=\pm \sqrt{81} \\ w+4=\pm 9 \\ w=-4\pm 9 \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} w=-4+9=5 \\ w=-4-9=-13 \\ w=5,w=-13 \end{gathered}$$

Check the solutions. 

Substitute $w=5$

localid="1648833425441" $$\begin{gathered} w^2+8w=65 \\ (5{)}^2+8(5)\stackrel{?}{=}65 \\ 25+40\stackrel{?}{=}65 \\ 65=65True \end{gathered}$$

Substitute $w=-13$

$$\begin{gathered} w^2+8w=65 \\ (-13{)}^2+8(-13)\stackrel{?}{=}65 \\ 169-104\stackrel{?}{=}65 \\ 65=65True \end{gathered}$$