Solve 9=x^2*1/sqrt{256}

$$9= { x }^{ 2 } \times \frac{ 1 }{ \sqrt{ 256 } }$$

Solve for x

$$x=12$$

$$x=-12$$

Steps Using Difference of Squares

Calculate the square root of 256 and get 16.

$$9=x^{2}\times \frac{1}{16}$$

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

$$x^{2}\times \frac{1}{16}=9$$

Subtract 9 from both sides.

$$x^{2}\times \frac{1}{16}-9=0$$

Multiply both sides by 16.

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

Consider x^{2}-144. Rewrite x^{2}-144 as x^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-12\right)\left(x+12\right)=0$$

To find equation solutions, solve x-12=0 and x+12=0.

$$x=12 x=-12$$

Steps by Finding Square Root

Calculate the square root of 256 and get 16.

$$9=x^{2}\times \frac{1}{16}$$

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

$$x^{2}\times \frac{1}{16}=9$$

Multiply both sides by 16, the reciprocal of \frac{1}{16}.

$$x^{2}=9\times 16$$

Multiply 9 and 16 to get 144.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

Calculate the square root of 256 and get 16.

$$9=x^{2}\times \frac{1}{16}$$

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

$$x^{2}\times \frac{1}{16}=9$$

Subtract 9 from both sides.

$$x^{2}\times \frac{1}{16}-9=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{1}{16}x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{16} for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{16}\left(-9\right)}}{2\times \frac{1}{16}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{16}\left(-9\right)}}{2\times \frac{1}{16}}$$

Multiply -4 times \frac{1}{16}.

$$x=\frac{0±\sqrt{-\frac{1}{4}\left(-9\right)}}{2\times \frac{1}{16}}$$

Multiply -\frac{1}{4} times -9.

$$x=\frac{0±\sqrt{\frac{9}{4}}}{2\times \frac{1}{16}}$$

Take the square root of \frac{9}{4}.

$$x=\frac{0±\frac{3}{2}}{2\times \frac{1}{16}}$$

Multiply 2 times \frac{1}{16}.

$$x=\frac{0±\frac{3}{2}}{\frac{1}{8}}$$

Now solve the equation x=\frac{0±\frac{3}{2}}{\frac{1}{8}} when ± is plus.

$$x=12$$

Now solve the equation x=\frac{0±\frac{3}{2}}{\frac{1}{8}} when ± is minus.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$