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)

Answer 1

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**.