Question

What would be the best method to use in order to solve the following quadratic equation?

4x^2+29x−60=0

a)Factoring

b)Quadratic Formula

c)Taking the Square Root

d)Completing the Square

Answer 1

Quadratic Formula
a=4
b=29
c=-60

x = -29 +- sq root(841 -4*4*-60) / 2*4
x = -29 +- sq root(841 +960) / 8
x = -29 +- sq root(1,801) / 8
x = [-29 +- 42.4381903478] / 8

x1 = 13.4381903478 / 8
x1 = 1.6797737935

x2 = [-29 - 42.4381903478] / 8
x2 = -71.4381903478 / 8
x2 = -8.9297737935

Answer 2

b) Quadratic Formula

Explanation:

The given expression is :

`4x^(2) +29x-60=0`

We will solve this by using Quadratic Equation Formula.

When the equation is in the form of
`ax^(2) +bx+c=0` we use the formula:

`x1 =\frac{-b+\sqrt{b^(2)-4ac}}{2a}` and
`x2 =\frac{-b-\sqrt{b^(2)-4ac}}{2a}`

Here a = 4, b = 29 and c = -60

Putting these in formula we get:

`x1 =\frac{-29+\sqrt{29^(2)-4*4*(-60)}}{2(4)}` and

`x2 =\frac{-29-\sqrt{29^(2)-4*4*(-60)}}{2(4)}`

Solving these we get,

`x1=(-29+√(1801))/(8)` and

`x2=(-29-√(1801))/(8)`

The final answer are :

x1=1.6797

x2=-8.9297

So, the quadratic formula is used here.

Factorization is not possible as the given equation is not a perfect square.

Taking the Square Root method will also not work here as this method helps when the expression contains only
`x^(2)` term.