x^2+5x+1=0 =x^2+5x+1 1=0 1 =1 1+5x+x^2=0 1 =5x+x^2=0 1 =x^2+5x= 1 coeff of x is 5. Take 5/2 , square it amp; add it on both sid ...

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Factorise : ...

Question

Factorise :
$x^{2} + 5 x + 1$

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Solution

$x^{2} + 5 x + 1 = 0$
$= x^{2} + 5 x + 1 - 1 = 0 - 1$
$= 1 - 1 + 5 x + x^{2} = 0 - 1$
$= 5 x + x^{2} = 0 - 1$
$= x^{2} + 5 x = - 1$
coeff of x is 5. Take $\frac{5}{2}$ , square it & add it on both sides
$= 5 x + 6.25 + x^{2} = - 1 + 6.25$
$= 6.25 + 5 x + x^{2} = 5.25$
$= (x + 2.5) (x + 2.5) = 5.25$
$∴ x + 2.5 = 2.29$
$x = - 0.208$
or
$x + 2.5 = - 2.29$
$x = - 4.79$

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