Solve y+3=(21/2-2x)^2

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

Solve for y

$$y=\frac{\left(5-4x\right)^{2}-12}{4}$$

Solution Steps

Multiply 2 and 2 to get 4.

$$y+3=\left(\frac{4+1}{2}-2x\right)^{2}$$

Add 4 and 1 to get 5.

$$y+3=\left(\frac{5}{2}-2x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{5}{2}-2x\right)^{2}.

$$y+3=\frac{25}{4}-10x+4x^{2}$$

Subtract 3 from both sides.

$$y=\frac{25}{4}-10x+4x^{2}-3$$

Subtract 3 from \frac{25}{4} to get \frac{13}{4}.

$$y=\frac{13}{4}-10x+4x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y+3}}{2}+\frac{5}{4}$$

$$x=-\frac{\sqrt{y+3}}{2}+\frac{5}{4}$$

Solve for x

$$x=\frac{\sqrt{y+3}}{2}+\frac{5}{4}$$

$$x=-\frac{\sqrt{y+3}}{2}+\frac{5}{4}\text{, }y\geq -3$$