Solve by Factoring 25x^2+30x+9=0

$25 x^{2} + 30 x + 9 = 0$

Step 1

Factor using the perfect square rule.

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

${(5 x)}^{2} + 30 x + 9 = 0$

Rewrite $9$ as $3^{2}$ .

${(5 x)}^{2} + 30 x + 3^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$30 x = 2 \cdot (5 x) \cdot 3$

Rewrite the polynomial.

${(5 x)}^{2} + 2 \cdot (5 x) \cdot 3 + 3^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 x$ and $b = 3$ .

${(5 x + 3)}^{2} = 0$

Step 2

Set the $5 x + 3$ equal to $0$ .

$5 x + 3 = 0$

Step 3

Solve for $x$ .

Subtract $3$ from both sides of the equation.

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

$\frac{5 x}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 3}{5}$

Divide $x$ by $1$ .

$x = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{5}$