Solve 2*6*16=x^2-12^2

$$2 \times 6 \times 16 = x ^ { 2 } - 12 ^ { 2 }$$

Solve for x

$$x=4\sqrt{21}\approx 18.33030278$$

$$x=-4\sqrt{21}\approx -18.33030278$$

Steps by Finding Square Root

Multiply 2 and 6 to get 12.

$$12\times 16=x^{2}-12^{2}$$

Multiply 12 and 16 to get 192.

$$192=x^{2}-12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$192=x^{2}-144$$

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

$$x^{2}-144=192$$

Add 144 to both sides.

$$x^{2}=192+144$$

Add 192 and 144 to get 336.

$$x^{2}=336$$

Take the square root of both sides of the equation.

$$x=4\sqrt{21} x=-4\sqrt{21}$$

Steps Using the Quadratic Formula

Multiply 2 and 6 to get 12.

$$12\times 16=x^{2}-12^{2}$$

Multiply 12 and 16 to get 192.

$$192=x^{2}-12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$192=x^{2}-144$$

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

$$x^{2}-144=192$$

Subtract 192 from both sides.

$$x^{2}-144-192=0$$

Subtract 192 from -144 to get -336.

$$x^{2}-336=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -336 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-336\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-336\right)}}{2}$$

Multiply -4 times -336.

$$x=\frac{0±\sqrt{1344}}{2}$$

Take the square root of 1344.

$$x=\frac{0±8\sqrt{21}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{21}}{2} when ± is plus.

$$x=4\sqrt{21}$$

Now solve the equation x=\frac{0±8\sqrt{21}}{2} when ± is minus.

$$x=-4\sqrt{21}$$

The equation is now solved.

$$x=4\sqrt{21} x=-4\sqrt{21}$$