Where Along the Y-Axis is the Electric Field Zero?

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SUMMARY

The electric field along the y-axis is zero at a specific point determined by the charges of -4.84 µC at the origin and -6.22 µC at 1.361 m. The relationship between the distances from each charge to the point where the electric field is zero is established using Coulomb's law. The equation kQ/r² = kq/(d-r)² simplifies to Q(d-r)² = qr², leading to the quadratic form d²/r² - 2d/r + 1 = q/Q. The user requires assistance in solving for the distance r from the origin where the electric field is zero.

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A charge of -4.84 [tex]\mu C[/tex] is located at the origin, and a charge of -6.22 [tex]\mu C[/tex] is located along the y-axis at 1.361 m. The value of the Coulomb constant is 8.99 x 10^9. At what point along the y-axis is the electric field zero. Answer in units of m.
I know that for the electric field to be zero, the electric field on the charges must equal each other.
I called the distance from the charge at the origin R, and the distance from the second point is d-r.
I used the equation for electric field and set them equal to each other.
[tex]kQ/r^2= kq/(d-r)^2[/tex]
[tex]Q/r^2 = q/ (d-r)^2[/tex]
[tex]Q(d-r)^2 =qr^2[/tex]
[tex](d-r)^2 =qr^2/ Q[/tex]
[tex](d^2 -2dr + r^2)/ r^2 = q/Q[/tex]
[tex]d^2/r^2 - 2d/r +1 = q/Q[/tex]
At this point I got stuck on how to solve for r, can someone help me?
Thanks in advance.
 
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Here's some help
[tex](d-r)^2 =qr^2/ Q[/tex]
[tex]d-r = r \sqrt{\frac{q}{Q}}[/tex]
 

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