Question

Solve this equation using all three methods 4x^ = 9

1.Factoring, 2. Complete the square, and 3. Using the Quadratic formula.

Answer 1

Answer:

$x=-\frac{3}{2}, x=\frac{3}{2}$

Step-by-step explanation:

(1)       To solve by factoring,

Given equation: $4 x^{2}=9$

Subtract 9 from both sides of the equation.

$\begin{aligned}&4 x^{2}-9=9-9\\&4 x^{2}-9=0\\&(2 x)^{2}-3^{2}=0\\&(2 x-3)(2 x+3)=0\end{aligned}$

Using zero factor principle, $2 x-3=0,2 x+3=0$

The solutions are $x=-\frac{3}{2}, x=\frac{3}{2}$.

(2) To solve by complete the square ,

Given $4 x^{2}=9$

Divide both sides of the equation by 4.  

$\frac{4 x^{2}}{4}=\frac{9}{4}$  

$\Rightarrow x^{2}=\frac{9}{4}$  

Square root on both sides.

$\Rightarrow x=\pm \frac{3}{2}$

$x=-\frac{3}{2}, x=\frac{3}{2}$

(3) To solve by quadratic formula,  

$4 x^{2}-9=0$

Here, a = 4, b = 0, c = –9

Quadratic formula, $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$x=\frac{-0 \pm \sqrt{0^{2}-4 \times 4 \times(-9)}}{2 \times 4}$

$\begin{aligned}&\Rightarrow x=\frac{\pm \sqrt{144}}{8}\\&\Rightarrow x=\pm \frac{3}{2}\\&\Rightarrow x=\frac{3}{2}, x=-\frac{3}{2}\end{aligned}$