Question

Solve the equation by completing square method.

$x^2-16x=-16$

Short answer

The solutions are$x=8\pm 4\sqrt{3}$.

Step-by-step solution

Given Information     

The Given equation is$x^2-16x=-16$.

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

The variable terms are on the left side.

$x^2-16x=-16$

Here, $b=-16$

So,

$$\begin{gathered} ={\left(\frac{1}{2}b\right)}^2 \\ ={\left(\frac{1}{2}(-16)\right)}^2 \\ ={\left(-8\right)}^2 \\ =64 \end{gathered}$$

Add $64$to both sides.

$$\begin{gathered} x^2-16x+64=-16+64 \\ {x}^2-16x+64=48 \end{gathered}$$

Factor the perfect square trinomial as a binomial square.    

$(x-8{)}^2=48$

Use the square root property.

$$\begin{gathered} x-8=\pm \sqrt{48} \\ x-8=\pm \sqrt{2\times 2\times 2\times 2\times 3} \\ x-8=\pm 4\sqrt{3} \\ x=8\pm 4\sqrt{3} \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} x=8+4\sqrt{3}, \\ x=8-4\sqrt{3} \end{gathered}$$