Question

Which would be the best method to use to solve the following equations? Explain your reasoning.

Use each method only once.

Factoring
Square root Property
Completing the square
Quadratic Formula

A. 3x^2-192=0
Method:
Why:

B. x^2-x-6=0
Method:
Why:

C. x^-6x-7=0
Method:
Why:

D. x^2-17x-7=0
Method:
Why:​

Answer 1

A. square root property

`3x^2-192=0\\x^2-66=0\\x^2=66\\x= -√(66) or √(66)`

it has one value with x which is x^2 and it cn be easily solved without having to factorise, quadratic formula cant be used as it need ax^2+bx+c=0 format

B. factorising

`x^2-x-6=0\\x^2+2x-3x-6=0\\(x+2)(x-3)=0\\x+2=0 and x-3=0\\x= -2 \\x= 3`

i just felt like this was easier to factorise than the other 2 options left

C. Completing the square

`x^2-6x-7=0\\(x-3)^2=0\\x= -1\\x= 7`

same reason personal preference

D- Quadratic

`x^2-17x-7=0\\x=(-(-17)+√((-17)^2-4(1)(-7)) )/(2(1)) \\x=(-(-17)-√((-17)^2-4(1)(-7)) )/(2(1))\\x=17.4\\x=-0.402`

the 17 kinda threw me off and i didnt wanna get on factorising or doing completing the square so quadratic formal