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Arte-miy333 [17]
3 years ago
8

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

Mathematics
1 answer:
Assoli18 [71]3 years ago
3 0

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}.

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If you look closely in the picture, you can see that:

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