What is (5-sqrt(x-2))^2 ?

The solution to (5-sqrt(x-2))^2 is x-10sqrt(x-2)+23

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simplify (5-sqrt(x-2))^2

simplify

(5 - x - 2)^{2}

x - 10 x - 2 + 23

Solution steps

(5 - x - 2)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(5 - x - 2)^{2} = 5^{2} - 2 \cdot 5 x - 2 + (x - 2)^{2}

= 5^{2} - 2 \cdot 5 x - 2 + (x - 2)^{2}

Simplify

5^{2} - 2 \cdot 5 x - 2 + (x - 2)^{2} : x - 10 x - 2 + 23

= x - 10 x - 2 + 23

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