Evaluate Using the Given Value 1/2(x^2+4)x=6

$\frac{1}{2} (x^{2} + 4) x = 6$

Step 1

Simplify $\frac{1}{2} \cdot ((x^{2} + 4) x)$ .

Apply the distributive property.

$\frac{1}{2} \cdot (x^{2} x + 4 x) = 6$

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{1}{2} \cdot (x^{2} x^{1} + 4 x) = 6$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2} \cdot (x^{2 + 1} + 4 x) = 6$

Add $2$ and $1$ .

$\frac{1}{2} \cdot (x^{3} + 4 x) = 6$

Apply the distributive property.

$\frac{1}{2} x^{3} + \frac{1}{2} (4 x) = 6$

Combine $\frac{1}{2}$ and $x^{3}$ .

$\frac{x^{3}}{2} + \frac{1}{2} (4 x) = 6$

Cancel the common factor of $2$ .

Factor $2$ out of $4 x$ .

$\frac{x^{3}}{2} + \frac{1}{2} (2 (2 x)) = 6$

Cancel the common factor.

$\frac{x^{3}}{2} + \frac{1}{2} (2 (2 x)) = 6$

Rewrite the expression.

$\frac{x^{3}}{2} + 2 x = 6$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.72244819$

Step 3