Solve G(1)s=49/s^2+4*2s+49

$$G ( 1 ) s = \frac { 49 } { s ^ { 2 } + 4 \cdot 2 s + 49 }$$

Solve for G

$$G=\frac{49}{s\left(s^{2}+8s+49\right)}$$

$$s\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by s^{2}+8s+49.

$$G\times 1s\left(s^{2}+8s+49\right)=49$$

Use the distributive property to multiply G\times 1s by s^{2}+8s+49.

$$Gs^{3}+8Gs^{2}+49G\times 1s=49$$

Multiply 49 and 1 to get 49.

$$Gs^{3}+8Gs^{2}+49Gs=49$$

Combine all terms containing G.

$$\left(s^{3}+8s^{2}+49s\right)G=49$$

Divide both sides by s^{3}+8s^{2}+49s.

$$\frac{\left(s^{3}+8s^{2}+49s\right)G}{s^{3}+8s^{2}+49s}=\frac{49}{s^{3}+8s^{2}+49s}$$

Dividing by s^{3}+8s^{2}+49s undoes the multiplication by s^{3}+8s^{2}+49s.

$$G=\frac{49}{s^{3}+8s^{2}+49s}$$

Divide 49 by s^{3}+8s^{2}+49s.

$$G=\frac{49}{s\left(s^{2}+8s+49\right)}$$

Solve for s

$$s=\frac{2^{\frac{2}{3}}\left(\sqrt[3]{21G\sqrt{3\left(6468G^{2}+5008G+1323\right)}+2504G|G|+1323|G|}+\sqrt[3]{-21G\sqrt{3\left(6468G^{2}+5008G+1323\right)}+2504G|G|+1323|G|}-8\sqrt[3]{2G|G|}\right)}{6\sqrt[3]{G|G|}}$$