Is this correct:
Problem #13
Solve: 9x^2 = 14
I did the following
i divided 9 by both sides then i get this:
x^2 = 1.5555555
then i squared both sides and i got the following answer:
x = 1.24
I would not have used decimals
x^2 = 14/9
x= +/- (√14)/3
Yes, except you actually took the square root of both sides. Remember in taking the square root, you get a +- answer.
To solve the equation 9x^2 = 14, you made a good attempt at solving it. Let's go through the steps together to make sure everything is clear.
Step 1: Divide both sides of the equation by 9 to isolate x^2.
(9x^2)/9 = 14/9
x^2 = 14/9
Step 2: Now, to find the value of x, you need to take the square root of both sides of the equation.
√(x^2) = ±√(14/9)
When you take the square root, you should consider both positive and negative roots since squaring a negative number also gives a positive result. This is why we have ±√(14/9).
Step 3: Simplify the square root of 14/9.
±√(14/9) can be further simplified as ±(√14)/√(9).
Since the square root of 9 is 3, the equation becomes:
x = ±(√14)/3.
So, the correct solution to the problem is x = ±(√14)/3.