x^2+r^2x^2=(1-r^2)x^2

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Solution for x^2+r^2x^2=(1-r^2)x^2 equation: 


Simplifying
x2 + r2x2 = (1 + -1r2) * x2

Reorder the terms:
r2x2 + x2 = (1 + -1r2) * x2

Reorder the terms for easier multiplication:
r2x2 + x2 = x2(1 + -1r2)
r2x2 + x2 = (1 * x2 + -1r2 * x2)

Reorder the terms:
r2x2 + x2 = (-1r2x2 + 1x2)
r2x2 + x2 = (-1r2x2 + 1x2)

Solving
r2x2 + x2 = -1r2x2 + 1x2

Solving for variable 'r'.

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

Add 'r2x2' to each side of the equation.
r2x2 + r2x2 + x2 = -1r2x2 + r2x2 + 1x2

Combine like terms: r2x2 + r2x2 = 2r2x2
2r2x2 + x2 = -1r2x2 + r2x2 + 1x2

Combine like terms: -1r2x2 + r2x2 = 0
2r2x2 + x2 = 0 + 1x2
2r2x2 + x2 = 1x2

Add '-1x2' to each side of the equation.
2r2x2 + x2 + -1x2 = 1x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2r2x2 + 0 = 1x2 + -1x2
2r2x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
2r2x2 = 0

Divide each side by '2'.
r2x2 = 0

Simplifying
r2x2 = 0

The solution to this equation could not be determined.

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