What are the solutions to the equation x^2-2x+a^2-1=0 ?

The solutions to the equation x^2-2x+a^2-1=0 are x=1+sqrt(-a^2+2),x=1-sqrt(-a^2+2)

Find the zeros of x^2-2x+a^2-1=0

The zeros of x^2-2x+a^2-1=0 are x=1+sqrt(-a^2+2),x=1-sqrt(-a^2+2)

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x^{2} - 2 x + a^{2} - 1 = 0

x = 1 + - a^{2} + 2, x = 1 - - a^{2} + 2

Solution steps

x^{2} - 2 x + a^{2} - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( a ^{2} - 1 )}{2 \cdot 1}

Simplify

(- 2)^{2} - 4 \cdot 1 \cdot (a^{2} - 1) : 2 - a^{2} + 2

x_{1, 2} = \frac{- ( - 2 ) \pm 2 - a ^{2} + 2}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 - a ^{2} + 2}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 2 - a ^{2} + 2}{2 \cdot 1}

x = \frac{- ( - 2 ) + 2 - a ^{2} + 2}{2 \cdot 1} : 1 + - a^{2} + 2

x = \frac{- ( - 2 ) - 2 - a ^{2} + 2}{2 \cdot 1} : 1 - - a^{2} + 2

The solutions to the quadratic equation are:

x = 1 + - a^{2} + 2, x = 1 - - a^{2} + 2

- 2 x^{2} + 4 x - 3 = 0

- x^{2} - 4 x + 6 = 0

5 x^{2} + 20 x + 17

4 x^{2} - x = 8

4 x^{2} - 10 x + 4 = 0

What are the solutions to the equation x^2-2x+a^2-1=0 ?
The solutions to the equation x^2-2x+a^2-1=0 are x=1+sqrt(-a^2+2),x=1-sqrt(-a^2+2)
Find the zeros of x^2-2x+a^2-1=0
The zeros of x^2-2x+a^2-1=0 are x=1+sqrt(-a^2+2),x=1-sqrt(-a^2+2)