Solve for x x2=14
Responses
x=±18
x equals plus or minus 1 eighth
x=±12
x equals plus or minus 1 half
x=±116
x equals plus or minus 1 sixteenth
x=±2
The Correct Answer and Explanation is:
To solve for ( x ) in the equation ( x^2 = 14 ), we need to isolate ( x ). The equation is a simple quadratic equation.
Step 1: Begin with the given equation
[
x^2 = 14
]
Step 2: Take the square root of both sides
Since ( x^2 ) equals 14, to solve for ( x ), we take the square root of both sides:
[
x = \pm \sqrt{14}
]
Step 3: Simplify the square root
The square root of 14 is approximately 3.74. Since there are no perfect squares involved, the square root cannot be simplified further. Therefore, we get:
[
x = \pm 3.74
]
This means that ( x ) can be either a positive or a negative value, and the solutions are approximately ( x = +3.74 ) or ( x = -3.74 ).
Explanation of the Options:
Let’s examine the options given in the problem:
- x = ±18: This is not correct because ( \sqrt{14} ) is approximately 3.74, not 18.
- x equals plus or minus 1 eighth: This is incorrect because 1/8 is a much smaller value than the square root of 14.
- x = ±12: This is incorrect. ( \sqrt{14} ) is approximately 3.74, so ±12 is not the correct solution.
- x = ±116: Again, this is incorrect because the square root of 14 is not as large as 116.
- x = ±2: This is also incorrect. The square root of 14 is not 2.
Therefore, none of the provided options are correct solutions to the equation. The actual solution is ( x = \pm \sqrt{14} ), which is approximately ( x = \pm 3.74 ).
Conclusion:
The correct solution to ( x^2 = 14 ) is ( x = \pm \sqrt{14} ), which approximates to ( x = \pm 3.74 ).