Question

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

Answer 1

`p=6+2 √(5), p=6-2 √(5)`

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((-12)/(2)\right)^(2)` on both sides of the equation.

`\Rightarrow p^(2)-12 p+\left((-12)/(2)\right)^(2)=-16+\left((-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 √(20)`

`p=6 \pm 2 √(5)`

Hence,
`p=6+2 √(5), p=6-2 √(5)`.