Need help ASAP. Quadratic Equa.

Question

You must choose a different algebraic method for solving each equation below. Explain the method you would use, as well as why you would use that method.

1. 2x^2-5x-12=0
2. x^2=24
3. x^2+8x+8=0

Answer 1

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 .

2x² -5x - 12= 0

factorize,

2x²- 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. x² = 24

x = √ 24 ( square root of 24 )

x = √ 4 * 6

x = 2√6

from no 3 eauation x²+ 8x + 8 = 0

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

The general form of quadratic equation is ax²+ bx + c = 0

and the formula to find x ,

so here above quadratic equation given x² + 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 ± √( 8²- 4*1* 8)

2* 1

x = -8 ±√ ( 64 - 32)

2

eliminating the denominator 2, we get

x = -4 ±√(32).....

Answer 2

(2x+3)(x-8) =0

x = -3/2, 8

x=sqr24 =+ or - 2sqr6

x^2 + 8x + 16 = -8+16

(x+4)^2 = 8

x+4 = sqr8

x = -4 + or - 2sqr2

factor the first, because it's easy to factor, relatively

just take the square root of the 2nd, because it's the simplest method for this problem,

complete the square or use the quadratic formula on the 3rd. because you can't factor it, and you can't take the square root as given.