Question

LOTS OF POINTS!!

What would be the best method to use in order to solve the following quadratic equations? 
1. x^2-3x=10
2. 4x^2+29x-60=0
3. x^2-6x=0
4. 5x^2+5=9x

Please choose from completing the square, factoring, quadratic, formula, taking the square root

Answer 1

See below

Explanation:

Problem 1

`x^2-3x=10` can be written as
`x^2-3x-10=0` and easily factors into
`(x-5)(x+2)=0` on the LHS, so factoring is best.

Problem 2

`4x^2+29x-60=0` can't be factored, so using the quadratic formula is the better way to go. Completing the square in this case would be too arduous, so I wouldn't recommend it.

Problem 3

`x^2-6x=0` can be factored on the LHS as
`x(x-6)=0` and it's easy to get the solutions, so factoring is best.

Problem 4

`5x^2+5=9x` can be written as
`5x^2-9x+5=0` and is best to use the quadratic formula since it can't be factored.

Answer 2

All of the methods you mentioned can be used to solve quadratic equations. However, some methods may be more efficient than others depending on the specific equation. Here’s a brief overview of when each method might be most useful:

Completing the square can be used to solve any quadratic equation and is a good method to use when the coefficient of the x^2 term is 1.

Factoring can be used when the quadratic equation can be easily factored into two binomials.

The quadratic formula can be used to solve any quadratic equation and is a good method to use when the other methods are difficult to apply.

Taking the square root can be used when the quadratic equation can be written in the form (x-a)^2=b.