Solve x^2+13/2x+169/16=y+113/

$${ x }^{ 2 } + \frac{ 13 }{ 2 } x+ \frac{ 169 }{ 16 } =y+ \frac{ 113 }{ }$$

Solve for y

$$y=x^{2}+\frac{13x}{2}-\frac{1639}{16}$$

Solution Steps

Anything divided by one gives itself.

$$x^{2}+\frac{13}{2}x+\frac{169}{16}=y+113$$

Swap sides so that all variable terms are on the left hand side.

$$y+113=x^{2}+\frac{13}{2}x+\frac{169}{16}$$

Subtract 113 from both sides.

$$y=x^{2}+\frac{13}{2}x+\frac{169}{16}-113$$

Subtract 113 from \frac{169}{16} to get -\frac{1639}{16}.

$$y=x^{2}+\frac{13}{2}x-\frac{1639}{16}$$

Solve for x (complex solution)

$$x=\sqrt{y+113}-\frac{13}{4}$$

$$x=-\sqrt{y+113}-\frac{13}{4}$$

Solve for x

$$x=\sqrt{y+113}-\frac{13}{4}$$

$$x=-\sqrt{y+113}-\frac{13}{4}\text{, }y\geq -113$$