What are the solutions to the equation solvefor x,x^2-4x+1=0 ?

The solutions to the equation solvefor x,x^2-4x+1=0 are x=2+sqrt(3),x=2-sqrt(3)

Find the zeros of solvefor x,x^2-4x+1=0

The zeros of solvefor x,x^2-4x+1=0 are x=2+sqrt(3),x=2-sqrt(3)

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x, x^{2} - 4 x + 1 = 0

x = 2 + 3, x = 2 - 3

Decimal Notation

x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

x^{2} - 4 x + 1 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 1 \cdot 1 = 23

x_{1, 2} = \frac{- ( - 4 ) \pm 2 3}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2 3}{2 \cdot 1}, x_{2} = \frac{- ( - 4 ) - 2 3}{2 \cdot 1}

x = \frac{- ( - 4 ) + 2 3}{2 \cdot 1} : 2 + 3

x = \frac{- ( - 4 ) - 2 3}{2 \cdot 1} : 2 - 3

The solutions to the quadratic equation are:

x = 2 + 3, x = 2 - 3

x^{2} - 6 x + 1

0 = 3 x^{2} - 12 x - 15

19 x = 7 - 6 x^{2}

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

36 x^{2} = - 25

What are the solutions to the equation solvefor x,x^2-4x+1=0 ?
The solutions to the equation solvefor x,x^2-4x+1=0 are x=2+sqrt(3),x=2-sqrt(3)
Find the zeros of solvefor x,x^2-4x+1=0
The zeros of solvefor x,x^2-4x+1=0 are x=2+sqrt(3),x=2-sqrt(3)