Solve the equation using square roots
2x^2-128=0
A. -sqrt8, sqrt 8
B. -64 or 64
C. -8 or 8
D. No real number solutions
I am stuck between A and C and i also have another problem similer to this one and its the same thing i am confused as do i leave the sqaure root on or no.
2x^2 - 128 = 0
x^2 = 64
x = ±√64 = ±8
To solve the equation 2x^2 - 128 = 0 using square roots, we need to isolate the variable x and then apply the square root to both sides of the equation.
Step 1: Add 128 to both sides of the equation to eliminate the constant term:
2x^2 = 128
Step 2: Divide both sides of the equation by 2 to isolate the variable x:
x^2 = 64
Step 3: Take the square root of both sides of the equation. Remember to consider both the positive and negative square roots:
x = ±√64
Simplifying the square root of 64 gives us:
x = ±8
Therefore, the correct answer is C. -8 or 8.
Regarding your question about leaving the square root on or not, typically in math problems like this, you would simplify the square root if possible. In this case, the square root of 64 is a whole number, so it can be simplified to ±8.
To solve the equation 2x^2 - 128 = 0 using square roots, we need to isolate the variable x. Here's how you can do it:
Step 1: Add 128 to both sides of the equation to eliminate the constant term:
2x^2 = 128
Step 2: Divide both sides by 2 to isolate the x^2 term:
x^2 = 64
Step 3: Take the square root of both sides of the equation. Remember that when taking the square root, we consider both the positive and negative square roots:
√(x^2) = ±√64
Step 4: Simplify the square root of 64:
x = ±8
So, the solution to the equation 2x^2 - 128 = 0 using square roots is x = ±8.
Now, to address your confusion about leaving the square root on or not: When we solve an equation using square roots, it is conventional to simplify the square roots unless stated otherwise. In this case, the correct answer would be option C, -8 or 8, because it is the simplified form of ±8.
Similarly, for your other problem, you should simplify the square roots unless instructed otherwise. If the options provided are fully simplified, then choose the option that matches your simplified answer.