Mamata G. answered • 10/05/20

Experienced and dedicated Math tutor in any grade level..

** Hi Chelsea .T** Here You have 3 eaquations I am trying to explain details 3 different types of equations and their different solving for x methods , hope those will help you .

2x^{2 }-5x - 12= 0

factorize,

2x^{2}- 8x + 3x - 12= 0

2x( x - 4 ) +3 ( x- 4 ) = 0

( x-4 ) ( 2x + 3 ) = 0

x-4 = 0

adding 4 both sides we get,

x = 4

Or 2x + 3 = 0

subtracting 3 from both sides we get ,

2x = -3

dividing by 2 both sides,

x = -3/2......

** From the first equation by Factorization we get either x= 4 or x= -3/2**

** **From second eqn. x^{2} = 24

x = √ 24 ( square root of 24 )

** ** x = √ 4 * 6

** x = 2√6**

from no 3 eauation x^{2}+ 8x + 8 = 0

Its a quadratic equation , so we can apply the formula of x

The general form of quadratic equation is ax^{2}+ bx + c = 0

and the formula to find x ,

so here above quadratic equation given x^{2} + 8x + 8 = 0 , our value of a = 1 , b = 8 and c= 8

plugging in all the values of a, b , c in the formula above

x= __-8 ± √( 8__^{2}__- 4*1* 8)__

2* 1

x =__ -8 ±√ ( 64 - 32) __

2

eliminating the denominator 2, we get

** x = -4 ±√(32)..... **