Solve by Factoring 16x(x-2)=8x-25

$16 x (x - 2) = 8 x - 25$

Step 1

Move all the expressions to the left side of the equation.

Subtract $8 x$ from both sides of the equation.

$16 x (x - 2) - 8 x = - 25$

Add $25$ to both sides of the equation.

$16 x (x - 2) - 8 x + 25 = 0$

Step 2

Simplify $16 x (x - 2) - 8 x + 25$ .

Simplify each term.

Apply the distributive property.

$16 x \cdot x + 16 x \cdot - 2 - 8 x + 25 = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$16 (x \cdot x) + 16 x \cdot - 2 - 8 x + 25 = 0$

Multiply $x$ by $x$ .

$16 x^{2} + 16 x \cdot - 2 - 8 x + 25 = 0$

Multiply $- 2$ by $16$ .

$16 x^{2} - 32 x - 8 x + 25 = 0$

Subtract $8 x$ from $- 32 x$ .

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

Step 3

Factor using the perfect square rule.

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

${(4 x)}^{2} - 40 x + 25 = 0$

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

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

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

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

Rewrite the polynomial.

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

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

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

Step 4

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

$4 x - 5 = 0$

Step 5

Solve for $x$ .

Add $5$ to both sides of the equation.

$4 x = 5$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Solve by Factoring 16x(x-2)=8x-25

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