Solve y=1(x-3.5)^2-90.25

$$y = 1 ( x - 3.5 ) ^ { 2 } - 90.25$$

Solve for y

$$y=\left(x-13\right)\left(x+6\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3.5\right)^{2}.

$$y=1\left(x^{2}-7x+12.25\right)-90.25$$

Use the distributive property to multiply 1 by x^{2}-7x+12.25.

$$y=x^{2}-7x+12.25-90.25$$

Subtract 90.25 from 12.25 to get -78.

$$y=x^{2}-7x-78$$

Solve for x (complex solution)

$$x=-\sqrt{y+90.25}+3.5$$

$$x=\sqrt{y+90.25}+3.5$$

Solve for x

$$x=\frac{-\sqrt{4y+361}+7}{2}$$

$$x=\frac{\sqrt{4y+361}+7}{2}\text{, }y\geq -\frac{361}{4}$$