Question

(p-4)^2=4p complete the square if possible

Answer 1

Answer:

$p=6+2 \sqrt{5}, p=6-2 \sqrt{5}$

Step-by-step explanation:

Step 1: Given expression is $(p-4)^{2}=4 p$.

Step 2: To write the equation in the quadratic form, subtract 4p from both sides of the equation.

$\Rightarrow(p-4)^{2}-4 p=4 p-4 p$

$\Rightarrow p^{2}-8 p+16-4 p=0$

$\Rightarrow p^{2}-12 p+16=0$

$\Rightarrow p^{2}-12 p=-16$

Step 3 :Add$\left(\frac{-12}{2}\right)^{2}$ on both sides of the equation.

$\Rightarrow p^{2}-12 p+\left(\frac{-12}{2}\right)^{2}=-16+\left(\frac{-12}{2}\right)^{2}$

$\Rightarrow p^{2}-12 p+36=-16+36$

$\Rightarrow(p-6)^{2}=20$

Step 4: Taking square root on both sides of the equation.

$(p-6)=\pm \sqrt{20}$

$p=6 \pm 2 \sqrt{5}$

Hence, $p=6+2 \sqrt{5}, p=6-2 \sqrt{5}$.