Solve 3x^2+14x=-11

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{11}{3}, x_{2} = - 1

Alternative Form

x_{1} = - 3. \dot{6}, x_{2} = - 1

Evaluate

3 x^{2} + 14 x = - 11

Move the expression to the left side

3 x^{2} + 14 x + 11 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 14 x + 11

Rewrite the expression

3 x^{2} + (11 + 3) x + 11

Calculate

3 x^{2} + 11 x + 3 x + 11

Rewrite the expression

x \times 3 x + x \times 11 + 3 x + 11

Factor out x from the expression

x (3 x + 11) + 3 x + 11

Factor out 3 x + 11 from the expression

(x + 1) (3 x + 11)

(x + 1) (3 x + 11) = 0

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

x + 1 = 0 3 x + 11 = 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 + 11 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 11 = 0

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

3 x = 0 - 11

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

3 x = - 11

Divide both sides

\frac{3 x}{3} = \frac{- 11}{3}

Divide the numbers

x = \frac{- 11}{3}

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

x = - \frac{11}{3}

x = - 1 x = - \frac{11}{3}

Solution

x_{1} = - \frac{11}{3}, x_{2} = - 1

Alternative Form

x_{1} = - 3. \dot{6}, x_{2} = - 1

Show Solution