Solve 9a^2 - 12a - 5

Question

Factor the expression

(3 a - 5) (3 a + 1)

Evaluate

9 a^{2} - 12 a - 5

Rewrite the expression

9 a^{2} + (3 - 15) a - 5

Calculate

9 a^{2} + 3 a - 15 a - 5

Rewrite the expression

3 a \times 3 a + 3 a - 5 \times 3 a - 5

Factor out 3 a from the expression

3 a (3 a + 1) - 5 \times 3 a - 5

Factor out - 5 from the expression

3 a (3 a + 1) - 5 (3 a + 1)

Solution

(3 a - 5) (3 a + 1)

Show Solution

a_{1} = - \frac{1}{3}, a_{2} = \frac{5}{3}

Alternative Form

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

Evaluate

9 a^{2} - 12 a - 5

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

9 a^{2} - 12 a - 5 = 0

Factor the expression

More Steps

Evaluate

9 a^{2} - 12 a - 5

Rewrite the expression

9 a^{2} + (3 - 15) a - 5

Calculate

9 a^{2} + 3 a - 15 a - 5

Rewrite the expression

3 a \times 3 a + 3 a - 5 \times 3 a - 5

Factor out 3 a from the expression

3 a (3 a + 1) - 5 \times 3 a - 5

Factor out - 5 from the expression

3 a (3 a + 1) - 5 (3 a + 1)

Factor out 3 a + 1 from the expression

(3 a - 5) (3 a + 1)

(3 a - 5) (3 a + 1) = 0

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

3 a - 5 = 0 3 a + 1 = 0

Solve the equation for a

More Steps

Evaluate

3 a - 5 = 0

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

3 a = 0 + 5

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

3 a = 5

Divide both sides

\frac{3 a}{3} = \frac{5}{3}

Divide the numbers

a = \frac{5}{3}

a = \frac{5}{3} 3 a + 1 = 0

Solve the equation for a

More Steps

Evaluate

3 a + 1 = 0

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

3 a = 0 - 1

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

3 a = - 1

Divide both sides

\frac{3 a}{3} = \frac{- 1}{3}

Divide the numbers

a = \frac{- 1}{3}

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

a = - \frac{1}{3}

a = \frac{5}{3} a = - \frac{1}{3}

Solution

a_{1} = - \frac{1}{3}, a_{2} = \frac{5}{3}

Alternative Form

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

Show Solution