Question

x^2 + 25x -306 =0 completing square method​

Answer 1

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Roots \ are \ 9 \ and -34}$

$\sf\orange{Given:}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{x^{2}+25x-306=0}}$

$\sf\pink{To \ find:}$

$\sf{The \ roots \ of \ the \ equation.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{The \ given \ quadratic \ equation \ is}$

$\sf{\implies{x^{2}+25x-306=0}}$

$\sf{\implies{Here, \ Coefficient \ of \ x^{2}=1}}$

$\sf{\implies{Coefficient \ of \ x=25}}$

$\sf{\implies{Constant=-306}}$

$\sf{\implies{x^{2}+25x=306}}$

_______________________________

$\sf{\implies{(\frac{1}{2}\times \ Coefficient \ of \ x)^{2}}}$

$\sf{\implies{(\frac{1}{2}\times25)^{2}}}$

$\sf{\implies{(\frac{25}{2})^{2}}}$

$\sf{\implies{\frac{625}{4}}}$

_______________________________

$\sf{Add \ \frac{625}{4} \ on \ both \ sides}$

$\sf{\implies{x^{2}+25x+\frac{625}{4}=306+\frac{625}{4}}}$

$\sf{\implies{x^{2}+25x+\frac{625}{4}=\frac{1224+625}{4}}}$

$\sf{\implies{(x+\frac{25}{2})^{2}=\frac{1849}{4}}}$

$\sf{Taking \ square \ root \ of \ both \ sides}$

$\sf{\implies{x+\frac{25}{2}=\frac{43}{2} \ or \ -\frac{43}{2}}}$

$\sf{\implies{x=\frac{43}{2}-\frac{25}{2} \ or \ -\frac{43}{2}-\frac{25}{2}}}$

$\sf{\implies{x=\frac{18}{2} \ or \ -\frac{68}{2}}}$

$\sf{\implies{x=9 \ or \ -34}}$

$\sf\purple{\tt{\therefore{Roots \ are \ 9 \ and -34}}}$