What are the solutions to the equation 2x^2-6x-11=0 ?

The solutions to the equation 2x^2-6x-11=0 are x=(3+sqrt(31))/2 ,x=(3-sqrt(31))/2

Find the zeros of 2x^2-6x-11=0

The zeros of 2x^2-6x-11=0 are x=(3+sqrt(31))/2 ,x=(3-sqrt(31))/2

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2 x^{2} - 6 x - 11 = 0

x = \frac{3 + 31}{2}, x = \frac{3 - 31}{2}

Decimal Notation

x = 4.28388 \dots, x = - 1.28388 \dots

Solution steps

2 x^{2} - 6 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 ( - 11 )}{2 \cdot 2}

(- 6)^{2} - 4 \cdot 2 (- 11) = 231

x_{1, 2} = \frac{- ( - 6 ) \pm 2 31}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 31}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 31}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 31}{2 \cdot 2} : \frac{3 + 31}{2}

x = \frac{- ( - 6 ) - 2 31}{2 \cdot 2} : \frac{3 - 31}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 31}{2}, x = \frac{3 - 31}{2}

x + 2 = (x - 5) (x + 2)

2 x^{2} + 5 x = - 6

0 = 2 x^{2} - 3 x + 1

12 x^{2} + 1 = 0

x, x^{2} - 6 x = 0

What are the solutions to the equation 2x^2-6x-11=0 ?
The solutions to the equation 2x^2-6x-11=0 are x=(3+sqrt(31))/2 ,x=(3-sqrt(31))/2
Find the zeros of 2x^2-6x-11=0
The zeros of 2x^2-6x-11=0 are x=(3+sqrt(31))/2 ,x=(3-sqrt(31))/2