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

Answer:

b) Quadratic Formula

Step-by-step 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:

$x1 =\frac{-29+\sqrt{29^{2}-4\times4\times(-60)}}{2(4)}$ and

$x2 =\frac{-29-\sqrt{29^{2}-4\times4\times(-60)}}{2(4)}$

Solving these we get,

$x1=\frac{-29+\sqrt{1801}}{8}$ and

$x2=\frac{-29-\sqrt{1801}}{8}$

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.