What is (sqrt(x-2)+7)^2 ?

The solution to (sqrt(x-2)+7)^2 is x+14sqrt(x-2)+47

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simplify (sqrt(x-2)+7)^2

simplify

(x - 2 + 7)^{2}

x + 14 x - 2 + 47

Solution steps

(x - 2 + 7)^{2}

Apply Perfect Square Formula:

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

(x - 2 + 7)^{2} = (x - 2)^{2} + 2 x - 2 \cdot 7 + 7^{2}

= (x - 2)^{2} + 2 x - 2 \cdot 7 + 7^{2}

Simplify

(x - 2)^{2} + 2 x - 2 \cdot 7 + 7^{2} : x + 14 x - 2 + 47

= x + 14 x - 2 + 47

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