MATH SOLVE

3 months ago

Q:
# What is the first step in solving the quadratic equation x2 = 9/16

Accepted Solution

A:

The equation is [tex]\displaystyle{ x^2= \frac{9}{16} [/tex]. We can rewrite the equation as:

[tex]\displaystyle{ x^2= (\frac{3}{4})^2[/tex].

Our next step here is to take the square root of both sides, remembering that [tex] \sqrt{x^2}=|x|[/tex].

Thus, we have [tex]\displaystyle{ |x|= \frac{3}{4}[/tex]. Our final step is solving the absolute value equation, which yields:

[tex]\displaystyle{ x= \frac{3}{4}[/tex] or [tex]\displaystyle{ x= -\frac{3}{4}[/tex].

Solution set: { [tex]-\frac{3}{4}, \frac{3}{4}[/tex] }

[tex]\displaystyle{ x^2= (\frac{3}{4})^2[/tex].

Our next step here is to take the square root of both sides, remembering that [tex] \sqrt{x^2}=|x|[/tex].

Thus, we have [tex]\displaystyle{ |x|= \frac{3}{4}[/tex]. Our final step is solving the absolute value equation, which yields:

[tex]\displaystyle{ x= \frac{3}{4}[/tex] or [tex]\displaystyle{ x= -\frac{3}{4}[/tex].

Solution set: { [tex]-\frac{3}{4}, \frac{3}{4}[/tex] }