Solve 3x^2 - 5x - 2 = 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} = 2

Alternative Form

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

Evaluate

3 x^{2} - 5 x - 2 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 5 x - 2

Rewrite the expression

3 x^{2} + (1 - 6) x - 2

Calculate

3 x^{2} + x - 6 x - 2

Rewrite the expression

x \times 3 x + x - 2 \times 3 x - 2

Factor out x from the expression

x (3 x + 1) - 2 \times 3 x - 2

Factor out - 2 from the expression

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

Factor out 3 x + 1 from the expression

(x - 2) (3 x + 1)

(x - 2) (3 x + 1) = 0

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

x - 2 = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

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

Solution

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

Alternative Form

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

Show Solution