What are the solutions to the equation m^2x^2+2mx+1-n^2=0 ?

The solutions to the equation m^2x^2+2mx+1-n^2=0 are x=(-1+n)/m ,x=-(n+1)/m ;\quad m\ne 0

Find the zeros of m^2x^2+2mx+1-n^2=0

The zeros of m^2x^2+2mx+1-n^2=0 are x=(-1+n)/m ,x=-(n+1)/m ;\quad m\ne 0

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m^{2} x^{2} + 2 m x + 1 - n^{2} = 0

x = \frac{- 1 + n}{m}, x = - \frac{n + 1}{m}; m \neq = 0

Solution steps

m^{2} x^{2} + 2 m x + 1 - n^{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 2 m \pm ( 2 m ) ^{2} - 4 m ^{2} ( 1 - n ^{2} )}{2 m ^{2}}

Simplify

(2 m)^{2} - 4 m^{2} (1 - n^{2}) : 2 mn

x_{1, 2} = \frac{- 2 m \pm 2 mn}{2 m ^{2}}; m \neq = 0

Separate the solutions

x_{1} = \frac{- 2 m + 2 mn}{2 m ^{2}}, x_{2} = \frac{- 2 m - 2 mn}{2 m ^{2}}

x = \frac{- 2 m + 2 mn}{2 m ^{2}} : \frac{- 1 + n}{m}

x = \frac{- 2 m - 2 mn}{2 m ^{2}} : - \frac{n + 1}{m}

The solutions to the quadratic equation are:

x = \frac{- 1 + n}{m}, x = - \frac{n + 1}{m}; m \neq = 0

a^{2} + 5^{2} = 1 0^{2}

(x - 5) (x - 1) = 0

x^{2} - 18 x - 10 = 0

4 x^{2} + 16 x + 18 = 0

3 x^{2} + 11 x + 8 = 0

What are the solutions to the equation m^2x^2+2mx+1-n^2=0 ?
The solutions to the equation m^2x^2+2mx+1-n^2=0 are x=(-1+n)/m ,x=-(n+1)/m ;\quad m\ne 0
Find the zeros of m^2x^2+2mx+1-n^2=0
The zeros of m^2x^2+2mx+1-n^2=0 are x=(-1+n)/m ,x=-(n+1)/m ;\quad m\ne 0