What are the solutions to the equation 1/2 x^2-x-1/3 =0 ?

The solutions to the equation 1/2 x^2-x-1/3 =0 are x=(3+sqrt(15))/3 ,x=(3-sqrt(15))/3

Find the zeros of 1/2 x^2-x-1/3 =0

The zeros of 1/2 x^2-x-1/3 =0 are x=(3+sqrt(15))/3 ,x=(3-sqrt(15))/3

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\frac{1}{2} x^{2} - x - \frac{1}{3} = 0

x = \frac{3 + 15}{3}, x = \frac{3 - 15}{3}

Decimal Notation

x = 2.29099 \dots, x = - 0.29099 \dots

Solution steps

\frac{1}{2} x^{2} - x - \frac{1}{3} = 0

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{1}{2} x^{2} \cdot 6 - x \cdot 6 - \frac{1}{3} \cdot 6 = 0 \cdot 6

Simplify

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 ( - 2 )}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 (- 2) = 215

x_{1, 2} = \frac{- ( - 6 ) \pm 2 15}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 15}{2 \cdot 3}, x_{2} = \frac{- ( - 6 ) - 2 15}{2 \cdot 3}

x = \frac{- ( - 6 ) + 2 15}{2 \cdot 3} : \frac{3 + 15}{3}

x = \frac{- ( - 6 ) - 2 15}{2 \cdot 3} : \frac{3 - 15}{3}

The solutions to the quadratic equation are:

x = \frac{3 + 15}{3}, x = \frac{3 - 15}{3}

1 + 4 + 7 + 3 n - 2 = \frac{n ( 3 n - 1 )}{2}

x (x + 10) = 8 (x + 1)

(x + 3) (x - 3) = x - 9

x, x^{2} + x = 0

- x^{2} - 4 x

What are the solutions to the equation 1/2 x^2-x-1/3 =0 ?
The solutions to the equation 1/2 x^2-x-1/3 =0 are x=(3+sqrt(15))/3 ,x=(3-sqrt(15))/3
Find the zeros of 1/2 x^2-x-1/3 =0
The zeros of 1/2 x^2-x-1/3 =0 are x=(3+sqrt(15))/3 ,x=(3-sqrt(15))/3