QQuestionMathematics
QuestionMathematics
Solve for $x$.
x^{2}= 14
Responses:
A. $x= \pm \sqrt{14}$
B. $x= \pm \frac{1}{8}$
C. $x= \pm \frac{1}{2}$
D. $x= \pm \frac{1}{16}$
E. $x= \pm 2$
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Answer
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Step 1:I'll solve this step-by-step following the exact LaTeX formatting guidelines:
Step 2:: Identify the equation
The equation is $$x^{2} = 14
Step 3:: Solve for x by taking the square root of both sides
x = \pm\sqrt{14}
To solve for x, we need to take the square root of both sides. Remember that when we take the square root, we get both positive and negative solutions.
Step 4:: Verify the solution
- When we square $$\pm\sqrt{14}$$, we get $$14$$, confirming our solution
- The right side is 14
Final Answer
The correct answer is A: x = \pm\sqrt{14} Key insights: - When solving x^{2} = a, the solution is always x = \pm\sqrt{a} - This gives two symmetric solutions around zero - Always check that squaring your solution returns the original equation
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