Question

Identify the most appropriate method to use to solve each quadratic equation: (a)$6a^2+14=20$

(b)${\left(x-\frac{1}{4}\right)}^2=\frac{5}{16}$

(c)$y^2-2y=8$

Short answer

(a) The most appropriate method to solve the equation $6a^2+14=20$is square root property.

(b) The most appropriate method to solve the equation ${\left(x-\frac{1}{4}\right)}^2=\frac{5}{16}$is square root property.

(c) The most appropriate method to solve the equation $y^2-2y=8$is Factoring.

Step-by-step solution

Part (a) Step 1: Given Information.  

The given equation is$6a^2+14=20$.

Part (a) Step 2: Identify the appropriate method to solve the given equation. 

$6a^2+14=20$

Rewrite in standard form.

$$\begin{gathered} 6a^2=20-14 \\ 6a^2=6 \end{gathered}$$

The equation is in the form of$a{x}^2=b$.

The appropriate method to solve this equation is square root property.

Part (b) Step 1: Given Information.  

The given equation is ${\left(x-\frac{1}{4}\right)}^2=\frac{5}{16}$.

Part (b) Step 2: Identify the appropriate method to solve the given equation.  

${\left(x-\frac{1}{4}\right)}^2=\frac{5}{16}$

The equation is in the form of $a(x-k{)}^2=h$.

The appropriate method to solve this equation is square root property.

Part (c) Step 1: Given Information.  

The given equation is $y^2-2y=8$.

Part (c) Step 2: Identify the appropriate method to solve the given equation.  

$y^2-2y=8$

Rewrite in standard form.

$y^2-2y-8=0$

We recognize that the left side of the equation is a perfect square trinomial, and so Factoring will be the most appropriate method.