Question

complex numbers unit test
how many real solutions does - 15x^2 - 3 = 2(7x^2 - 1.5) have? (1 point)
real solution(s)

Explanation:

Step1: Expand the right - hand side

Expand $2(7x^{2}-1.5)$ to get $14x^{2}-3$. So the equation becomes $- 15x^{2}-3=14x^{2}-3$.

Step2: Move all terms to one side

Add $15x^{2}$ to both sides and add 3 to both sides. We have $-15x^{2}+15x^{2}-3 + 3=14x^{2}+15x^{2}-3 + 3$, which simplifies to $0 = 29x^{2}$.

Step3: Solve for x

Divide both sides of $0 = 29x^{2}$ by 29 to get $x^{2}=0$. Then take the square - root of both sides. Using the property $\sqrt{x^{2}}=\vert x\vert$, we have $x = 0$.

Answer:

1