Solve y=(x+1.5)^2-30.25

$$y = ( x + 1.5 ) ^ { 2 } - 30.25$$

Solve for y

$$y=\left(x-4\right)\left(x+7\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1.5\right)^{2}.

$$y=x^{2}+3x+2.25-30.25$$

Subtract 30.25 from 2.25 to get -28.

$$y=x^{2}+3x-28$$

Solve for x (complex solution)

$$x=-\left(\sqrt{y+30.25}+1.5\right)$$

$$x=\sqrt{y+30.25}-1.5$$

Solve for x

$$x=\frac{-\sqrt{4y+121}-3}{2}$$

$$x=\frac{\sqrt{4y+121}-3}{2}\text{, }y\geq -\frac{121}{4}$$