Solve each equation by factoring.

7x²-243=0

I know I'm supposed to add 243 to the other side but don't know what else to do. Divide maybe?

Thanks in advance.

-243+7x^2= 0 (reorder)
-243+243+7x^2 = 0+243 (add 243 to both sides)
7x^2=243 (Combine like terms)
x^2=34.71428571 (Divide each side by 7/simplify)
-34.71428571+x^2=34.71428571 +-34.71428571(reorder)
-34.71428571+x^2=0.00000000
Answer: The solution to this equation can not be determined.

To solve the equation 7x²-243=0 by factoring, you start by rearranging the equation to have 0 on one side:

7x² - 243 = 0

Next, you want to factor the quadratic expression on the left side. However, this particular quadratic equation cannot be easily factored. Instead, you can try using the quadratic formula to find the solutions.

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this to our equation, we can see that a = 7, b = 0, and c = -243. Plugging these values into the quadratic formula:

x = (0 ± √(0² - 4(7)(-243))) / (2(7))

Simplifying further:

x = ± √(0 + 6804) / 14

x = ± √(6804) / 14

x = ± 82.64 / 14

x ≈ ±5.9

So the solutions to the equation 7x² - 243 = 0 are approximately x = -5.9 and x = 5.9.