Solve 3x^2 + 14x + 8 = 0

Question

Solve the quadratic equation

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

Alternative Form

x_{1} = - 4, x_{2} = - 0. \dot{6}

Evaluate

3 x^{2} + 14 x + 8 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 14 x + 8

Rewrite the expression

3 x^{2} + (2 + 12) x + 8

Calculate

3 x^{2} + 2 x + 12 x + 8

Rewrite the expression

x \times 3 x + x \times 2 + 4 \times 3 x + 4 \times 2

Factor out x from the expression

x (3 x + 2) + 4 \times 3 x + 4 \times 2

Factor out 4 from the expression

x (3 x + 2) + 4 (3 x + 2)

Factor out 3 x + 2 from the expression

(x + 4) (3 x + 2)

(x + 4) (3 x + 2) = 0

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

3 x + 2 = 0 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

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

Divide the numbers

x = \frac{- 2}{3}

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

x = - \frac{2}{3}

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

Solve the equation for x

More Steps

Evaluate

x + 4 = 0

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

x = 0 - 4

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

x = - 4

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

Solution

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

Alternative Form

x_{1} = - 4, x_{2} = - 0. \dot{6}

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