Solve x2 = 78 by inspection. What are the two real solutions?(1 point) Responses {−74, 74 } {−74, 74 } {−72, 72 } {−72, 72 } {−78, 78 } {−78, 78 } {−74, 7−4 }

Answer 1

To solve the equation \( x^2 = 78 \) by inspection, we can look for numbers whose square equals 78.

The solutions to the equation \( x^2 = 78 \) can be found as follows:

1. The positive solution is \( x = \sqrt{78} \).
2. The negative solution is \( x = -\sqrt{78} \).

Now, we can estimate the value of \( \sqrt{78} \). Since \( 8^2 = 64 \) and \( 9^2 = 81 \), we know that \( \sqrt{78} \) is between 8 and 9.

Calculating \( \sqrt{78} \) more accurately:

\[ \sqrt{78} \approx 8.83 \]

So, the two real solutions are approximately:

1. \( x \approx 8.83 \)
2. \( x \approx -8.83 \)

However, from your provided response options:

• None of the provided options accurately represent \( \pm\sqrt{78} \).

The correct solutions are:

• \( \sqrt{78} \) (approximately 8.83)
• \( -\sqrt{78} \) (approximately -8.83)

If you're looking for the closest whole numbers among your options, neither fits directly. However, the answer is not exactly in the options you provided. Should \( 74 \) or \( 72 \) have been provided as whole numbers, one could lead to confusion but they do not represent solutions to the original equation.

To sum up, the correct solutions are approximately \( 8.83 \) and \( -8.83 \).

Answer 2

So what’s the answer

Answer 3

The solutions to the equation \( x^2 = 78 \), by inspection, are \( x = \sqrt{78} \) and \( x = -\sqrt{78} \).

Approximating these values, we find:

• \( \sqrt{78} \approx 8.83 \)
• \( -\sqrt{78} \approx -8.83 \)

However, based on the options provided ({−74, 74}, {−72, 72}, {−78, 78}, {−74, 7−4}), it seems there is a misunderstanding or mistake, as none of the given options corresponds to the correct numerical values of the square roots of 78.

If you need a final answer among the provided options, the actual solutions \( \pm \sqrt{78} \) are approximately \( \pm 8.83\), which are not listed.

Please double-check the options or let me know if there is a specific range of solutions you are looking for based on those choices.