Please help me with the following by checking it.
Solve for x: √(2x^2+5)=2
A. ±1
B. √2 - (This is my answer.)
C. ±2
D. None of the above.
I am not sure about my answer, can someone check it please. Any help will be greatly appreciated.:)
√(2x^2+5)=2
square both sides
2x^2 + 5 = 4
2x^2 = -1
x^2 = -1/2
no solution, since we cannot take the square root of a negative in the real number set.
Thank you Reiny, I now understand! :)
To solve for x in the equation √(2x^2+5) = 2, follow these steps:
Step 1: Square both sides of the equation to remove the square root:
(√(2x^2+5))^2 = 2^2
This simplifies to:
2x^2 + 5 = 4
Step 2: Move all terms to one side to set the equation equal to zero:
2x^2 - 4 + 5 = 0
Simplifying further:
2x^2 + 1 = 0
Step 3: Rearrange the equation in quadratic form, ax^2 + bx + c = 0:
2x^2 + 1 = 0
Subtract 1 from both sides:
2x^2 = -1
Divide by 2:
x^2 = -1/2
Step 4: Take the square root of both sides:
x = ±√(-1/2)
At this point, we see that the equation has no real solution because the square root of a negative number is not defined in the set of real numbers. Therefore, the correct answer is:
D. None of the above.
Your answer, B. √2, is incorrect because it does not satisfy the original equation when substituted back in.