Question
What are the real solutions, if any, for −x2−2.5=−18.5%0D%0A−%0D%0A𝑥%0D%0A2%0D%0A−%0D%0A2.5%0D%0A=%0D%0A−%0D%0A18.5%0D%0A ?(1 point)%0D%0AResponses%0D%0A%0D%0Ax=±4%0D%0A𝑥%0D%0A=%0D%0A±%0D%0A4%0D%0Ax is equal to plus or minus 4%0D%0A%0D%0Ax=4%0D%0A𝑥%0D%0A=%0D%0A4%0D%0Ax is equal to 4%0D%0A%0D%0Ax=−4%0D%0A𝑥%0D%0A=%0D%0A−%0D%0A4%0D%0Ax is equal to negative 4%0D%0A%0D%0Ax=±4i
Answers
Answered by
GPT-4o mini
To solve the given equation:
\[
-\frac{x^2}{2.5} = -18.5
\]
First, we can eliminate the negative sign by multiplying both sides by -1:
\[
\frac{x^2}{2.5} = 18.5
\]
Next, multiply both sides by 2.5 to isolate \(x^2\):
\[
x^2 = 18.5 \times 2.5
\]
Calculating the right side:
\[
18.5 \times 2.5 = 46.25
\]
Now we have:
\[
x^2 = 46.25
\]
To find \(x\), we take the square root of both sides:
\[
x = \pm \sqrt{46.25}
\]
Calculating the square root:
\[
\sqrt{46.25} \approx 6.8
\]
So the real solutions are:
\[
x \approx \pm 6.8
\]
Among the choices presented in the original question, none seem to match the calculation. All values provided (±4, 4, -4, ±4i) do not equal ±6.8.
Therefore, the correct conclusion is that there are no real solutions among the provided options. The correct solutions, computed as approximately ±6.8, do not match any given options.
\[
-\frac{x^2}{2.5} = -18.5
\]
First, we can eliminate the negative sign by multiplying both sides by -1:
\[
\frac{x^2}{2.5} = 18.5
\]
Next, multiply both sides by 2.5 to isolate \(x^2\):
\[
x^2 = 18.5 \times 2.5
\]
Calculating the right side:
\[
18.5 \times 2.5 = 46.25
\]
Now we have:
\[
x^2 = 46.25
\]
To find \(x\), we take the square root of both sides:
\[
x = \pm \sqrt{46.25}
\]
Calculating the square root:
\[
\sqrt{46.25} \approx 6.8
\]
So the real solutions are:
\[
x \approx \pm 6.8
\]
Among the choices presented in the original question, none seem to match the calculation. All values provided (±4, 4, -4, ±4i) do not equal ±6.8.
Therefore, the correct conclusion is that there are no real solutions among the provided options. The correct solutions, computed as approximately ±6.8, do not match any given options.