Question
Solve x^2 = 25/64 for all real solutions
Enter the lower value solution first
Enter the lower value solution first
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 = \frac{25}{64} \), we take the square root of both sides. Remember, when we take the square root, we consider both the positive and the negative solutions.
\[
x = \pm \sqrt{\frac{25}{64}}
\]
Calculating the square root, we get:
\[
x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8}
\]
Thus, the solutions are:
\[
x = -\frac{5}{8} \quad \text{and} \quad x = \frac{5}{8}
\]
Entering the lower value solution first, the final answer is:
\[
-\frac{5}{8}, \frac{5}{8}
\]
\[
x = \pm \sqrt{\frac{25}{64}}
\]
Calculating the square root, we get:
\[
x = \pm \frac{\sqrt{25}}{\sqrt{64}} = \pm \frac{5}{8}
\]
Thus, the solutions are:
\[
x = -\frac{5}{8} \quad \text{and} \quad x = \frac{5}{8}
\]
Entering the lower value solution first, the final answer is:
\[
-\frac{5}{8}, \frac{5}{8}
\]