KnowledgeBoat Logo
|

Mathematics

Solve :

(x - 10) (1200x+2)=1260\Big(\dfrac{1200}{x} + 2\Big) = 1260 and x < 0

Quadratic Equations

2 Likes

Answer

Given,

⇒(x−10)(1200x+2)=1260⇒(x−10)(1200+2xx)=1260⇒(x−10)(1200+2x)=1260x⇒1200x+2x2−12000−20x=1260x⇒1180x+2x2−1260x−12000=0⇒2x2−80x−12000=0⇒2(x2−40x−6000)=0⇒x2−40x−6000=0⇒x2−100x+60x−6000=0⇒x(x−100)+60(x−100)=0⇒(x−100)(x+60)=0⇒x−100=0 or x+60=0⇒x=100 or x=−60.\Rightarrow (x - 10) \Big(\dfrac{1200}{x} + 2\Big) = 1260 \\[1em] \Rightarrow (x - 10)\Big(\dfrac{1200 + 2x}{x}\Big) = 1260 \\[1em] \Rightarrow (x - 10)(1200 + 2x) = 1260x \\[1em] \Rightarrow 1200x + 2x^2 - 12000 - 20x = 1260x \\[1em] \Rightarrow 1180x + 2x^2 - 1260x - 12000 = 0 \\[1em] \Rightarrow 2x^2 - 80x - 12000 = 0 \\[1em] \Rightarrow 2(x^2 - 40x - 6000) = 0 \\[1em] \Rightarrow x^2 - 40x - 6000 = 0 \\[1em] \Rightarrow x^2 - 100x + 60x - 6000 = 0 \\[1em] \Rightarrow x(x - 100) + 60(x - 100) = 0 \\[1em] \Rightarrow (x - 100)(x + 60) = 0 \\[1em] \Rightarrow x - 100 = 0 \text{ or } x + 60 = 0 \\[1em] \Rightarrow x = 100 \text{ or } x = -60.

Since, x < 0

∴ x = -60.

Hence, x = -60.

Answered By

2 Likes

Related Questions