Solve y=left(x+3right)^2*0.3-4

$$y= { \left(x+3 \right) }^{ 2 } \times 0.3-4$$

Solve for y

$$y=\frac{3\left(x+3\right)^{2}}{10}-4$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$y=\left(x^{2}+6x+9\right)\times 0.3-4$$

Use the distributive property to multiply x^{2}+6x+9 by 0.3.

$$y=0.3x^{2}+1.8x+2.7-4$$

Subtract 4 from 2.7 to get -1.3.

$$y=0.3x^{2}+1.8x-1.3$$

Solve for x (complex solution)

$$x=-\left(\sqrt{\frac{10y+40}{3}}+3\right)$$

$$x=\sqrt{\frac{10y+40}{3}}-3$$

Solve for x

$$x=-\frac{\sqrt{\frac{40y+160}{3}}}{2}-3$$

$$x=\frac{\sqrt{\frac{40y+160}{3}}}{2}-3\text{, }y\geq -4$$