Simplify x^2+1/2(20x^2-10x+6)+2x

$x^{2} + \frac{1}{2} (20 x^{2} - 10 x + 6) + 2 x$

Simplify each term.

Apply the distributive property.

$x^{2} + \frac{1}{2} (20 x^{2}) + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Simplify.

Cancel the common factor of $2$ .

Factor $2$ out of $20 x^{2}$ .

$x^{2} + \frac{1}{2} (2 (10 x^{2})) + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Cancel the common factor.

$x^{2} + \frac{1}{2} (2 (10 x^{2})) + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Rewrite the expression.

$x^{2} + 10 x^{2} + \frac{1}{2} (- 10 x) + \frac{1}{2} \cdot 6 + 2 x$

Cancel the common factor of $2$ .

Factor $2$ out of $- 10 x$ .

$x^{2} + 10 x^{2} + \frac{1}{2} (2 (- 5 x)) + \frac{1}{2} \cdot 6 + 2 x$

Cancel the common factor.

$x^{2} + 10 x^{2} + \frac{1}{2} (2 (- 5 x)) + \frac{1}{2} \cdot 6 + 2 x$

Rewrite the expression.

$x^{2} + 10 x^{2} - 5 x + \frac{1}{2} \cdot 6 + 2 x$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x^{2} + 10 x^{2} - 5 x + \frac{1}{2} \cdot (2 (3)) + 2 x$

Cancel the common factor.

$x^{2} + 10 x^{2} - 5 x + \frac{1}{2} \cdot (2 \cdot 3) + 2 x$

Rewrite the expression.

$x^{2} + 10 x^{2} - 5 x + 3 + 2 x$

Simplify by adding terms.

Add $x^{2}$ and $10 x^{2}$ .

$11 x^{2} - 5 x + 3 + 2 x$

Add $- 5 x$ and $2 x$ .

$11 x^{2} - 3 x + 3$