Solve 3x^2-2x-1=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{3}, x_{2} = 1

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 1

Evaluate

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

Factor the expression

More Steps

Evaluate

3 x^{2} - 2 x - 1

Rewrite the expression

3 x^{2} + (1 - 3) x - 1

Calculate

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

Rewrite the expression

x \times 3 x + x - 3 x - 1

Factor out x from the expression

x (3 x + 1) - 3 x - 1

Factor out - 1 from the expression

x (3 x + 1) - (3 x + 1)

Factor out 3 x + 1 from the expression

(x - 1) (3 x + 1)

(x - 1) (3 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

x - 1 = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x = 1

x = 1 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 1 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

3 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{3}

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

Solution

x_{1} = - \frac{1}{3}, x_{2} = 1

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 1

Show Solution