What are the solutions to the equation x^2-18x-3=0 ?

The solutions to the equation x^2-18x-3=0 are x=9+2sqrt(21),x=9-2sqrt(21)

Find the zeros of x^2-18x-3=0

The zeros of x^2-18x-3=0 are x=9+2sqrt(21),x=9-2sqrt(21)

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x^{2} - 18 x - 3 = 0

x = 9 + 221, x = 9 - 221

Decimal Notation

x = 18.16515 \dots, x = - 0.16515 \dots

Solution steps

x^{2} - 18 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 1 \cdot ( - 3 )}{2 \cdot 1}

(- 18)^{2} - 4 \cdot 1 \cdot (- 3) = 421

x_{1, 2} = \frac{- ( - 18 ) \pm 4 21}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 4 21}{2 \cdot 1}, x_{2} = \frac{- ( - 18 ) - 4 21}{2 \cdot 1}

x = \frac{- ( - 18 ) + 4 21}{2 \cdot 1} : 9 + 221

x = \frac{- ( - 18 ) - 4 21}{2 \cdot 1} : 9 - 221

The solutions to the quadratic equation are:

x = 9 + 221, x = 9 - 221

- 4 = (x - 3)^{2} - 4

2 x^{2} - 6 = - 206

(x + 1) (x - 2) = 3 (x - 2)

2 x^{2} - x - 20 = 0

x^{2} + b x = c

What are the solutions to the equation x^2-18x-3=0 ?
The solutions to the equation x^2-18x-3=0 are x=9+2sqrt(21),x=9-2sqrt(21)
Find the zeros of x^2-18x-3=0
The zeros of x^2-18x-3=0 are x=9+2sqrt(21),x=9-2sqrt(21)