What are the solutions to the equation 1003x^2+(1003+2sqrt(1001))x+199=0 ?

The solutions to the equation 1003x^2+(1003+2sqrt(1001))x+199=0 are

Find the zeros of 1003x^2+(1003+2sqrt(1001))x+199=0

The zeros of 1003x^2+(1003+2sqrt(1001))x+199=0 are

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1003 x^{2} + (1003 + 21001) x + 199 = 0

x = \frac{- 1003 - 2 1001 + 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}, x = \frac{- 1003 - 2 1001 - 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

Solution steps

1003 x^{2} + (1003 + 21001) x + 199 = 0

Divide both sides by

1003

\frac{1003 x ^{2}}{1003} + \frac{( 1003 + 2 1001 ) x}{1003} + \frac{199}{1003} = \frac{0}{1003}

Write in the standard form

a x^{2} + b x + c = 0

x^{2} + (1 + \frac{2 1001}{1003}) x + \frac{199}{1003} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 1 + \frac{2 1001}{1003} ) \pm ( 1 + \frac{2 1001}{1003} ) ^{2} - 4 \cdot 1 \cdot \frac{199}{1003}}{2 \cdot 1}

(1 + \frac{2 1001}{1003})^{2} - 4 \cdot 1 \cdot \frac{199}{1003} = \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}

x_{1, 2} = \frac{- ( 1 + \frac{2 1001}{1003} ) \pm \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( 1 + \frac{2 1001}{1003} ) + \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1}, x_{2} = \frac{- ( 1 + \frac{2 1001}{1003} ) - \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1}

x = \frac{- ( 1 + \frac{2 1001}{1003} ) + \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1} : \frac{- 1003 - 2 1001 + 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

x = \frac{- ( 1 + \frac{2 1001}{1003} ) - \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2 \cdot 1} : \frac{- 1003 - 2 1001 - 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

The solutions to the quadratic equation are:

x = \frac{- 1003 - 2 1001 + 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}, x = \frac{- 1003 - 2 1001 - 1003 \frac{1010013}{1006009} + \frac{4 1001 - 796}{1003}}{2006}

10 n^{2} + 11 n + 3

4 x^{2} - 7 = - 4 x

3^{2} - 3

(- 3 - - 7)^{2}

39 - \frac{6}{25}

What are the solutions to the equation 1003x^2+(1003+2sqrt(1001))x+199=0 ?
The solutions to the equation 1003x^2+(1003+2sqrt(1001))x+199=0 are
Find the zeros of 1003x^2+(1003+2sqrt(1001))x+199=0
The zeros of 1003x^2+(1003+2sqrt(1001))x+199=0 are