What are the solutions to the equation (x-3)^2+(x-1)^2=1 ?

The solutions to the equation (x-3)^2+(x-1)^2=1 are x=2+i(sqrt(2))/2 ,x=2-i(sqrt(2))/2

Find the zeros of (x-3)^2+(x-1)^2=1

The zeros of (x-3)^2+(x-1)^2=1 are x=2+i(sqrt(2))/2 ,x=2-i(sqrt(2))/2

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(x - 3)^{2} + (x - 1)^{2} = 1

x = 2 + i \frac{2}{2}, x = 2 - i \frac{2}{2}

Solution steps

(x - 3)^{2} + (x - 1)^{2} = 1

Expand

(x - 3)^{2} + (x - 1)^{2} : 2 x^{2} - 8 x + 10

2 x^{2} - 8 x + 10 = 1

Move

1

to the left side

2 x^{2} - 8 x + 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 2 \cdot 9}{2 \cdot 2}

Simplify

(- 8)^{2} - 4 \cdot 2 \cdot 9 : 22 i

x_{1, 2} = \frac{- ( - 8 ) \pm 2 2 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 2 2 i}{2 \cdot 2}, x_{2} = \frac{- ( - 8 ) - 2 2 i}{2 \cdot 2}

x = \frac{- ( - 8 ) + 2 2 i}{2 \cdot 2} : 2 + i \frac{2}{2}

x = \frac{- ( - 8 ) - 2 2 i}{2 \cdot 2} : 2 - i \frac{2}{2}

The solutions to the quadratic equation are:

x = 2 + i \frac{2}{2}, x = 2 - i \frac{2}{2}

x, 5 x^{2} + 2 y^{2} - 10 x + 4 y + 7 = 0

5 p^{2} + 5 p + 4 = 0

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

a^{2} = 1 7^{2} - 8^{2}

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

What are the solutions to the equation (x-3)^2+(x-1)^2=1 ?
The solutions to the equation (x-3)^2+(x-1)^2=1 are x=2+i(sqrt(2))/2 ,x=2-i(sqrt(2))/2
Find the zeros of (x-3)^2+(x-1)^2=1
The zeros of (x-3)^2+(x-1)^2=1 are x=2+i(sqrt(2))/2 ,x=2-i(sqrt(2))/2