How do you solve #4x^2-6=74#?

Question

Ethan Adkins · Accepted Answer

#x=2sqrt5#

We can begin by adding #6# to both sides of this equation. Doing this, we get:

#4x^2=80#

We want to isolate #x#, so the next best step would be to divide both sides by #4#. We get:

#x^2=20#

Now, we can take the square root of both sides to get:

#x=+-sqrt20# (We have a positive and negative answer because squaring a negative number will also result in a positive number)

We can factor out a perfect square from #+-sqrt20#. #20# is equal to #4*5#, so #sqrt20# will be equal to #sqrt4*sqrt5#. Now, we have:

#x=+-(color(blue)(sqrt4)*color(red)sqrt5)#

This simplifies to:

#x=+-color(blue)(2)color(red)sqrt5#

Eli Assouline · Answer

undefined To solve the equation 4x^2 - 6 = 74, you first add 6 to both sides to isolate the quadratic term. Then, you divide both sides by 4 to isolate the x^2 term. Next, you take the square root of both sides to solve for x. Finally, you simplify the equation to find the solutions. The steps are as follows:

1. Add 6 to both sides: 4x^2 = 80.
2. Divide both sides by 4: x^2 = 20.
3. Take the square root of both sides: x = ±√20.
4. Simplify the square root of 20: x = ±2√5.

Therefore, the solutions to the equation are x = ±2√5.