√(9 (2x+5)^2) =√(3^2 (2x+5)^2) =√((3 2x 5)(3+2x+5)) =√(( 2x 2)(8+2x)) =√( 2(x+1)2(4+x)) =√( 4)√((x+1)(x+4)) =2i√((x+1))√((x+4 ...

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Zeroes of a Polynomial

Solve √9-2x+...

Question

Solve
$\sqrt{9 - (2 x + 5)^{2}}$

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Solution

$\sqrt{9 - {(2 x + 5)}^{2}}$
$= \sqrt{3^{2} - {(2 x + 5)}^{2}}$
$= \sqrt{(3 - 2 x - 5) (3 + 2 x + 5)}$
$= \sqrt{(- 2 x - 2) (8 + 2 x)}$
$= \sqrt{- 2 (x + 1) 2 (4 + x)}$
$= \sqrt{- 4} \sqrt{(x + 1) (x + 4)}$
$= 2 i \sqrt{(x + 1)} \sqrt{(x + 4)}$

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