Question

Solve: sqrt(x+9) = x-3

Answer 1

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`√(x + 9) = x - 3`

Sides gets power 2

`({ √(x + 9) })^(2) = ( {x - 3})^(2)`

`|x + 9| = {x}^(2) - 6x + 9`

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`x + 9 = {x}^(2) - 6x + 9`

Subtract sides 9

`x + 9 - 9 = {x}^(2) - 6x + 9 - 9`

`x = {x}^(2) - 6x`

Subtract sides x

`x - x = {x}^(2) - 6x - x`

`{x}^(2) - 7x = 0`

`x(x - 7) = 0`

`x = 0`

OR

`x - 7 = 0`

`x = 7`

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`x + 9 = - ( {x}^(2) - 6x + 9)`

`x + 9 = - {x}^(2) + 6x - 9`

Subtract sides 9

`x + 9 - 9 = - {x}^(2) + 6x - 9 - 9 \\`

`x = - {x}^(2) + 6x - 18`

Subtract sides x

`x - x = - {x}^(2) + 6x - 18 - x`

`- {x}^(2) + 5x - 18 = 0`

Multiply sides by -1

`{x}^(2) - 5x + 18 = 0`

`x = No \: \: solution`

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CHECK the roots :

`x = 0`

`√(0 + 9) ≠0 - 3`

`√(9) ≠ - 3`

`3≠ - 3`

Thus (( x = 0 )) is unacceptable.

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`x = 7`

`√(7 + 9) = 7 - 3`

`√(16) = 4`

`4 = 4`

Thus (( x = 7 )) is the only solution for x.

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Done...

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Answer 2

The answer is (x-3) = 2 lol