2r^2+RS-s^2=0

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Solution for 2r^2+RS-s^2=0 equation: 


Simplifying
2r2 + RS + -1s2 = 0

Reorder the terms:
RS + 2r2 + -1s2 = 0

Solving
RS + 2r2 + -1s2 = 0

Solving for variable 'R'.

Move all terms containing R to the left, all other terms to the right.

Add '-2r2' to each side of the equation.
RS + 2r2 + -2r2 + -1s2 = 0 + -2r2

Combine like terms: 2r2 + -2r2 = 0
RS + 0 + -1s2 = 0 + -2r2
RS + -1s2 = 0 + -2r2
Remove the zero:
RS + -1s2 = -2r2

Add 's2' to each side of the equation.
RS + -1s2 + s2 = -2r2 + s2

Combine like terms: -1s2 + s2 = 0
RS + 0 = -2r2 + s2
RS = -2r2 + s2

Divide each side by 'S'.
R = -2r2S-1 + s2S-1

Simplifying
R = -2r2S-1 + s2S-1

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