Solve 9x^2 + 18x + 8

Question

Factor the expression

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

Evaluate

9 x^{2} + 18 x + 8

Rewrite the expression

9 x^{2} + (12 + 6) x + 8

Calculate

9 x^{2} + 12 x + 6 x + 8

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out 2 from the expression

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

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = - 0. \dot{6}

Evaluate

9 x^{2} + 18 x + 8

To find the roots of the expression,set the expression equal to 0

9 x^{2} + 18 x + 8 = 0

Factor the expression

More Steps

Evaluate

9 x^{2} + 18 x + 8

Rewrite the expression

9 x^{2} + (12 + 6) x + 8

Calculate

9 x^{2} + 12 x + 6 x + 8

Rewrite the expression

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

Factor out 3 x from the expression

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

Factor out 2 from the expression

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

Factor out 3 x + 4 from the expression

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

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

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

3 x + 2 = 0 3 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} 3 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 4 = 0

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

3 x = 0 - 4

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

3 x = - 4

Divide both sides

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

Divide the numbers

x = \frac{- 4}{3}

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

x = - \frac{4}{3}

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

Solution

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

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = - 0. \dot{6}

Show Solution