Solve 4.10^7=9.10^4*Q^2/0,3^2=

$$4.10 ^ { 7 } = \frac { 9.10 ^ { 4 } \cdot Q ^ { 2 } } { 0,3 ^ { 2 } } =$$

Solve for Q

$$Q=\frac{206763\sqrt{410}}{8281000}\approx 0.505570784$$

$$Q=-\frac{206763\sqrt{410}}{8281000}\approx -0.505570784$$

Steps by Finding Square Root

Calculate 4.1 to the power of 7 and get 19475.4273881.

$$19475.4273881=\frac{9.1^{4}Q^{2}}{0.3^{2}}$$

Calculate 9.1 to the power of 4 and get 6857.4961.

$$19475.4273881=\frac{6857.4961Q^{2}}{0.3^{2}}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$19475.4273881=\frac{6857.4961Q^{2}}{0.09}$$

Divide 6857.4961Q^{2} by 0.09 to get \frac{68574961}{900}Q^{2}.

$$19475.4273881=\frac{68574961}{900}Q^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{68574961}{900}Q^{2}=19475.4273881$$

Divide both sides by \frac{68574961}{900}.

$$Q^{2}=\frac{19475.4273881}{\frac{68574961}{900}}$$

Take the square root of both sides of the equation.

$$Q=\frac{206763\sqrt{410}}{8281000} Q=-\frac{206763\sqrt{410}}{8281000}$$

Steps Using the Quadratic Formula

Calculate 4.1 to the power of 7 and get 19475.4273881.

$$19475.4273881=\frac{9.1^{4}Q^{2}}{0.3^{2}}$$

Calculate 9.1 to the power of 4 and get 6857.4961.

$$19475.4273881=\frac{6857.4961Q^{2}}{0.3^{2}}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$19475.4273881=\frac{6857.4961Q^{2}}{0.09}$$

Divide 6857.4961Q^{2} by 0.09 to get \frac{68574961}{900}Q^{2}.

$$19475.4273881=\frac{68574961}{900}Q^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{68574961}{900}Q^{2}=19475.4273881$$

Subtract 19475.4273881 from both sides.

$$\frac{68574961}{900}Q^{2}-19475.4273881=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{68574961}{900} for a, 0 for b, and -19475.4273881 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$Q=\frac{0±\sqrt{0^{2}-4\times \frac{68574961}{900}\left(-19475.4273881\right)}}{2\times \frac{68574961}{900}}$$

Square 0.

$$Q=\frac{0±\sqrt{-4\times \frac{68574961}{900}\left(-19475.4273881\right)}}{2\times \frac{68574961}{900}}$$

Multiply -4 times \frac{68574961}{900}.

$$Q=\frac{0±\sqrt{-\frac{68574961}{225}\left(-19475.4273881\right)}}{2\times \frac{68574961}{900}}$$

Multiply -\frac{68574961}{225} times -19475.4273881 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$Q=\frac{0±\sqrt{\frac{13355266735972893641}{2250000000}}}{2\times \frac{68574961}{900}}$$

Take the square root of \frac{13355266735972893641}{2250000000}.

$$Q=\frac{0±\frac{570734801\sqrt{410}}{150000}}{2\times \frac{68574961}{900}}$$

Multiply 2 times \frac{68574961}{900}.

$$Q=\frac{0±\frac{570734801\sqrt{410}}{150000}}{\frac{68574961}{450}}$$

Now solve the equation Q=\frac{0±\frac{570734801\sqrt{410}}{150000}}{\frac{68574961}{450}} when ± is plus.

$$Q=\frac{206763\sqrt{410}}{8281000}$$

Now solve the equation Q=\frac{0±\frac{570734801\sqrt{410}}{150000}}{\frac{68574961}{450}} when ± is minus.

$$Q=-\frac{206763\sqrt{410}}{8281000}$$

The equation is now solved.

$$Q=\frac{206763\sqrt{410}}{8281000} Q=-\frac{206763\sqrt{410}}{8281000}$$