Solve by Factoring 49x^2+25=70x

$49 x^{2} + 25 = 70 x$

Step 1

Subtract $70 x$ from both sides of the equation.

$49 x^{2} + 25 - 70 x = 0$

Step 2

Factor using the perfect square rule.

Rearrange terms.

$49 x^{2} - 70 x + 25 = 0$

Rewrite $49 x^{2}$ as ${(7 x)}^{2}$ .

${(7 x)}^{2} - 70 x + 25 = 0$

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

${(7 x)}^{2} - 70 x + 5^{2} = 0$

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

$70 x = 2 \cdot (7 x) \cdot 5$

Rewrite the polynomial.

${(7 x)}^{2} - 2 \cdot (7 x) \cdot 5 + 5^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 7 x$ and $b = 5$ .

${(7 x - 5)}^{2} = 0$

Step 3

Set the $7 x - 5$ equal to $0$ .

$7 x - 5 = 0$

Step 4

Solve for $x$ .

Add $5$ to both sides of the equation.

$7 x = 5$

Divide each term in $7 x = 5$ by $7$ and simplify.

Divide each term in $7 x = 5$ by $7$ .

$\frac{7 x}{7} = \frac{5}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{5}{7}$

Divide $x$ by $1$ .

$x = \frac{5}{7}$