Solve 8^2*(16/3)^2=x^2

$$8 ^ { 2 } \cdot ( \frac { 16 } { 3 } ) ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{128}{3} = 42\frac{2}{3} \approx 42.666666667$$

$$x = -\frac{128}{3} = -42\frac{2}{3} \approx -42.666666667$$

Steps Using Difference of Squares

Calculate 8 to the power of 2 and get 64.

$$64\times \left(\frac{16}{3}\right)^{2}=x^{2}$$

Calculate \frac{16}{3} to the power of 2 and get \frac{256}{9}.

$$64\times \frac{256}{9}=x^{2}$$

Multiply 64 and \frac{256}{9} to get \frac{16384}{9}.

$$\frac{16384}{9}=x^{2}$$

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

$$x^{2}=\frac{16384}{9}$$

Subtract \frac{16384}{9} from both sides.

$$x^{2}-\frac{16384}{9}=0$$

Multiply both sides by 9.

$$9x^{2}-16384=0$$

Consider 9x^{2}-16384. Rewrite 9x^{2}-16384 as \left(3x\right)^{2}-128^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-128\right)\left(3x+128\right)=0$$

To find equation solutions, solve 3x-128=0 and 3x+128=0.

$$x=\frac{128}{3} x=-\frac{128}{3}$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64\times \left(\frac{16}{3}\right)^{2}=x^{2}$$

Calculate \frac{16}{3} to the power of 2 and get \frac{256}{9}.

$$64\times \frac{256}{9}=x^{2}$$

Multiply 64 and \frac{256}{9} to get \frac{16384}{9}.

$$\frac{16384}{9}=x^{2}$$

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

$$x^{2}=\frac{16384}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{128}{3} x=-\frac{128}{3}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64\times \left(\frac{16}{3}\right)^{2}=x^{2}$$

Calculate \frac{16}{3} to the power of 2 and get \frac{256}{9}.

$$64\times \frac{256}{9}=x^{2}$$

Multiply 64 and \frac{256}{9} to get \frac{16384}{9}.

$$\frac{16384}{9}=x^{2}$$

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

$$x^{2}=\frac{16384}{9}$$

Subtract \frac{16384}{9} from both sides.

$$x^{2}-\frac{16384}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{16384}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16384}{9}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{16384}{9}\right)}}{2}$$

Multiply -4 times -\frac{16384}{9}.

$$x=\frac{0±\sqrt{\frac{65536}{9}}}{2}$$

Take the square root of \frac{65536}{9}.

$$x=\frac{0±\frac{256}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{256}{3}}{2} when ± is plus.

$$x=\frac{128}{3}$$

Now solve the equation x=\frac{0±\frac{256}{3}}{2} when ± is minus.

$$x=-\frac{128}{3}$$

The equation is now solved.

$$x=\frac{128}{3} x=-\frac{128}{3}$$