What are the solutions to the equation (x+1/3)(x-1/3)= 1/3 ?

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

Find the zeros of (x+1/3)(x-1/3)= 1/3

The zeros of (x+1/3)(x-1/3)= 1/3 are x= 2/3 ,x=-2/3

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(x + \frac{1}{3}) (x - \frac{1}{3}) = \frac{1}{3}

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

Decimal Notation

x = 0.66666 \dots, x = - 0.66666 \dots

Solution steps

(x + \frac{1}{3}) (x - \frac{1}{3}) = \frac{1}{3}

Multiply both sides by

3

3 (x + \frac{1}{3}) (x - \frac{1}{3}) = 1

Expand

3 (x + \frac{1}{3}) (x - \frac{1}{3}) : 3 x^{2} - \frac{1}{3}

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

Move

1

to the left side

3 x^{2} - \frac{4}{3} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 \cdot 3 ( - \frac{4}{3} )}{2 \cdot 3}

0^{2} - 4 \cdot 3 (- \frac{4}{3}) = 4

x_{1, 2} = \frac{- 0 \pm 4}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 0 + 4}{2 \cdot 3}, x_{2} = \frac{- 0 - 4}{2 \cdot 3}

x = \frac{- 0 + 4}{2 \cdot 3} : \frac{2}{3}

x = \frac{- 0 - 4}{2 \cdot 3} : - \frac{2}{3}

The solutions to the quadratic equation are:

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

x^{2} + 6 x = - x + 30

0 = 3 x^{2} + 6 x

x^{2} - 10 x + 2 = 0

(x - 3)^{2} + x (x + 2) = 9

3 x^{2} + 112 = 2 x^{2} + 22 x

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