Solve A^2=64+36-36*0.7071

$${ A }^{ 2 } = 64+36-36 \cdot 0.7071$$

Solve for A

$$A = \frac{\sqrt{186361}}{50} \approx 8.633909891$$

$$A = -\frac{\sqrt{186361}}{50} \approx -8.633909891$$

Steps by Finding Square Root

Add 64 and 36 to get 100.

$$A^{2}=100-36\times 0.7071$$

Multiply 36 and 0.7071 to get 25.4556.

$$A^{2}=100-25.4556$$

Subtract 25.4556 from 100 to get 74.5444.

$$A^{2}=74.5444$$

Take the square root of both sides of the equation.

$$A=\frac{\sqrt{186361}}{50} A=-\frac{\sqrt{186361}}{50}$$

Steps Using the Quadratic Formula

Add 64 and 36 to get 100.

$$A^{2}=100-36\times 0.7071$$

Multiply 36 and 0.7071 to get 25.4556.

$$A^{2}=100-25.4556$$

Subtract 25.4556 from 100 to get 74.5444.

$$A^{2}=74.5444$$

Subtract 74.5444 from both sides.

$$A^{2}-74.5444=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -74.5444 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{0±\sqrt{0^{2}-4\left(-74.5444\right)}}{2}$$

Square 0.

$$A=\frac{0±\sqrt{-4\left(-74.5444\right)}}{2}$$

Multiply -4 times -74.5444.

$$A=\frac{0±\sqrt{298.1776}}{2}$$

Take the square root of 298.1776.

$$A=\frac{0±\frac{\sqrt{186361}}{25}}{2}$$

Now solve the equation A=\frac{0±\frac{\sqrt{186361}}{25}}{2} when ± is plus.

$$A=\frac{\sqrt{186361}}{50}$$

Now solve the equation A=\frac{0±\frac{\sqrt{186361}}{25}}{2} when ± is minus.

$$A=-\frac{\sqrt{186361}}{50}$$

The equation is now solved.

$$A=\frac{\sqrt{186361}}{50} A=-\frac{\sqrt{186361}}{50}$$