Precalculus Examples

$25 x^{2} + 16 = 40 x$

Step 1

Subtract $40 x$ from both sides of the equation.

$25 x^{2} + 16 - 40 x = 0$

Step 2

Factor using the perfect square rule.

Tap for more steps...

Step 2.1

Rearrange terms.

$25 x^{2} - 40 x + 16 = 0$

Step 2.2

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

${(5 x)}^{2} - 40 x + 16 = 0$

Step 2.3

Rewrite $16$ as $4^{2}$ .

${(5 x)}^{2} - 40 x + 4^{2} = 0$

Step 2.4

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

$40 x = 2 \cdot (5 x) \cdot 4$

Step 2.5

Rewrite the polynomial.

${(5 x)}^{2} - 2 \cdot (5 x) \cdot 4 + 4^{2} = 0$

Step 2.6

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 x$ and $b = 4$ .

${(5 x - 4)}^{2} = 0$

Step 3

Set the $5 x - 4$ equal to $0$ .

$5 x - 4 = 0$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Add $4$ to both sides of the equation.

$5 x = 4$

Step 4.2

Divide each term in $5 x = 4$ by $5$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{5}$