Question

x ^2 -20x=-96=? solve it ​

Answer 1

$\large{\mathfrak{\underline{\underline{Answer:-}}}}$

x = 12 or 8

$\large{\mathfrak{\underline{\underline{Solution:-}}}}$

We have equation :-

x² - 20x = -96

____________________________

• 1st Method

[Splitting the middle term]

x² - 20x = -96

⇒ x² - 20x + 96 = 0

⇒ x² -12x -8x + 96 = 0

⇒ x(x - 12) -8(x - 12) = 0

⇒ (x - 12) (x - 8) = 0

So,

x can be 12 or 8 .

__________________________

• 2nd Method

[Quadratic formula]

$\huge{\boxed{\boxed{\bf{D \: = \: b^{2} \: - \: 4ac}}}}$

x² - 20x + 96 = 0

Where,

a = 1

b = -20

c = 96

___________________[Put Values]

D = (-20)² - 4(1)(96)

D = 400 - 384

D = 16

√D = 4

Now to find zeroes we have a formula :-

$\huge{\bf{\boxed{\boxed{x \: = \: {\frac{-b \: ± \: {\sqrt{D}}}{2a}}}}}}$

______________[Put values]

x = {-(-20) ± 4} / 2

x = (20 ± 4)/2

_________________________

Case 1

x = (20 + 4)/2

x = 24/2

x = 12

________________________

Case 2

x = (20 - 4)/2

x = 16/2

x = 8

_________________________

$\huge{\bf{\boxed{\boxed{x \: = \: 12 \: or \: 8}}}}$

Answer 2

SOLUTION:-

Given:

x² - 20x = -96

So,

We can find through the middle splitting term method:

⚫When splitting the middle term, our objective is to write quadratic expressions as the product of two linear polynomials.

Now, we have;

x² - 20x + 96= 0

=) x² -12x -8x + 96 =0

=) x(x-12) - 8(x-12) =0

=) (x-12)(x-8) =0

Solve:

x-12= 0

=) x= 12

Solve:

x -8 = 0

=) x= 8

Hence,

The value is 12 & 8.

Hope it helps ☺️