Question

solve 9x² - 155x - 500 using splitting the middle term​

Answer 1

GIVEN :–

• A quadratic equation 9x² - 155x - 500 = 0

TO FIND :–

• Find 'x' ( Using Splitting Middle term )

SOLUTION :–

$\\ \implies{ \bold{9 {x}^{2} - 155x - 500 = 0}}$

• Now Splitting Middle term –

$\\ \implies{ \bold{ 9{x}^{2} {\underbrace{- 180x + 25x}}- 500 = 0}}$

$\\ \implies{ \bold{ 9x(x - 20) + 25(x- 20) = 0}}$

$\\ \implies{ \bold{ (9x + 25)(x - 20)= 0}}$

• So that –

$\\ \implies{ \bold{ x - 20= 0}}$

$\\ \implies \large{ \boxed{ \bold{ x = 20}}}$

• And –

$\\ \implies{ \bold{ 9x + 25= 0}}$

$\\ \implies{ \bold{ 9x = - 25}}$

$\\ \implies \large{ \boxed{ \bold{ x = - \dfrac{ 25}{9}}}}$

• Hence , $\: \: { \bold{ x = 20\:,\: \left( - \dfrac{ 25}{9} \right) }} \: \:$

Answer 2

Step-by-step explanation:

${\red{\underline{\underline{\red{Given:-}}}}}$

• 9x² - 155x - 500

${\blue{\underline{\underline{\bold{To\: Find}}}}}$

• The value of 'x' by splitting the middle terms

${\green{\underline{\underline{\bold{Solution:-}}}}}$

$9 {x}^{2} - 155x - 500 \\ \\ \implies9 {x}^{2} - 180x + 25x - 500 \\ \\ \implies9x(x - 20) + 25(x - 20) \\ \\ \implies(9x + 25)(x - 20)\\ \\ \implies(9x + 25) = 0 \: \: \: (or) \: \: \: (x - 20) = 0$

____________

$9x + 25 = 0 \\ \\ \implies 9x = - 25 \\ \\ \implies x = \frac{ - 25}{9}$

_____________

$x - 20 = 0 \\ \\ \implies x = 20$

${\pink{\underline{\underline{\bold{Verification}}}}}$

Case 1:-

Substitute x = 20 in ( 9x² - 155x - 500 )

$9 {(20})^{2} - 155(20) - 500 = 0 \\ \\ \implies9(400) - 3100 - 500 = 0 \\ \\ \implies3600 - 3100 - 500 = 0 \\ \\ \implies500 - 500 = 0 \\ \\ \implies0 = 0$

L.H.S = R.H.S

Hence, proved

Therefore,

$\boxed{x = \frac{-25}{9} , \: 20}$