Question
Complex Numbers Unit Test
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Question
How many real solutions does −15x2−3=2(7x2−1.5)
have?(1 point)
real solution(s)
Answers
GPT-4o mini
To solve the equation \(-15x^2 - 3 = 2(7x^2 - 1.5)\), we first simplify the right side:
\[
2(7x^2 - 1.5) = 14x^2 - 3
\]
Now, rewrite the equation:
\[
-15x^2 - 3 = 14x^2 - 3
\]
Next, we can add \(3\) to both sides to eliminate the constants:
\[
-15x^2 = 14x^2
\]
Now, let's move all the terms involving \(x^2\) to one side:
\[
-15x^2 - 14x^2 = 0
\]
This simplifies to:
\[
-29x^2 = 0
\]
Now, divide both sides by \(-29\):
\[
x^2 = 0
\]
Taking the square root of both sides yields:
\[
x = 0
\]
Since this is the only solution, we have 1 real solution to the equation.
Thus, the number of real solutions is **1**.
\[
2(7x^2 - 1.5) = 14x^2 - 3
\]
Now, rewrite the equation:
\[
-15x^2 - 3 = 14x^2 - 3
\]
Next, we can add \(3\) to both sides to eliminate the constants:
\[
-15x^2 = 14x^2
\]
Now, let's move all the terms involving \(x^2\) to one side:
\[
-15x^2 - 14x^2 = 0
\]
This simplifies to:
\[
-29x^2 = 0
\]
Now, divide both sides by \(-29\):
\[
x^2 = 0
\]
Taking the square root of both sides yields:
\[
x = 0
\]
Since this is the only solution, we have 1 real solution to the equation.
Thus, the number of real solutions is **1**.