Solve 3x^(2) = -4x -1

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

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

Evaluate

3 x^{2} = - 4 x - 1

Move the expression to the left side

3 x^{2} + 4 x + 1 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 4 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 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

3 x + 1 = 0 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 = - \frac{1}{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 = - \frac{1}{3} x = - 1

Solution

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

Alternative Form

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

Show Solution