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

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

Step 1

Subtract $30 x$ from both sides of the equation.

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

Step 2

Factor using the perfect square rule.

Rearrange terms.

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

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

${(3 x)}^{2} - 30 x + 25 = 0$

Rewrite $25$ as $5^{2}$ .

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

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

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

Rewrite the polynomial.

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

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

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

Step 3

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

$3 x - 5 = 0$

Step 4

Solve for $x$ .

Add $5$ to both sides of the equation.

$3 x = 5$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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