Question

Solve for x

(x-5) ²+5 =49

Answer 1

`\left(x-5\right)^2+5=49`

Subtract 5 from both sides

`\left(x-5\right)^2+5-5=49-5`

`\left(x-5\right)^2=44`

`x-5=√(44)`

`44=2^(2) *11`

`x-5=√(11) \sqrt{2^(2) }`

Radical rule:-
`\sqrt[n]{a^(n) } =a`

`x-5=2√(11)`

Add 5 to both sides

`x=2√(11)+5`

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`x-5=-2√(11)`

Add 5 to both sides

`x-5=-2√(11)`

Ans:
`x=2√(11)+5,\:x=-2√(11)+5`

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Answer 2

x = 5±2 sqrt(11)

Explanation:

(x-5) ²+5 =49

Subtract 5 from each side

(x-5) ²+5-5 =49-5

(x-5) ² =44

Take the square root of each side

sqrt((x-5) ²) =±sqrt(44)

sqrt((x-5) ²) =±sqrt(4*11)

x-5 = ±2 sqrt(11)

Add 5 to each side

x-5+5 = 5±2 sqrt(11)

x = 5±2 sqrt(11)