Solve y=1/2x^2+3/2x+2quad1/2x

$$y = \frac { 1 } { 2 } x ^ { 2 } + \frac { 3 } { 2 } x + 2 \quad \frac { 1 } { 2 } x$$

Solve for y

$$y=\frac{x\left(x+8\right)}{2}$$

Solution Steps

Multiply 2 and 2 to get 4.

$$y=\frac{1}{2}x^{2}+\frac{3}{2}x+\frac{4+1}{2}x$$

Add 4 and 1 to get 5.

$$y=\frac{1}{2}x^{2}+\frac{3}{2}x+\frac{5}{2}x$$

Combine \frac{3}{2}x and \frac{5}{2}x to get 4x.

$$y=\frac{1}{2}x^{2}+4x$$

Solve for x (complex solution)

$$x=-\left(\sqrt{2\left(y+8\right)}+4\right)$$

$$x=\sqrt{2\left(y+8\right)}-4$$

Solve for x

$$x=-\left(\sqrt{2\left(y+8\right)}+4\right)$$

$$x=\sqrt{2\left(y+8\right)}-4\text{, }y\geq -8$$