Solve 4096=x^2

$$4096= { x }^{ 2 }$$

Solve for x

$$x=64$$

$$x=-64$$

Steps Using Difference of Squares

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

$$x^{2}=4096$$

Subtract 4096 from both sides.

$$x^{2}-4096=0$$

Consider x^{2}-4096. Rewrite x^{2}-4096 as x^{2}-64^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-64\right)\left(x+64\right)=0$$

To find equation solutions, solve x-64=0 and x+64=0.

$$x=64 x=-64$$

Steps by Finding Square Root

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

$$x^{2}=4096$$

Take the square root of both sides of the equation.

$$x=64 x=-64$$

Steps Using the Quadratic Formula

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

$$x^{2}=4096$$

Subtract 4096 from both sides.

$$x^{2}-4096=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4096 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4096\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4096\right)}}{2}$$

Multiply -4 times -4096.

$$x=\frac{0±\sqrt{16384}}{2}$$

Take the square root of 16384.

$$x=\frac{0±128}{2}$$

Now solve the equation x=\frac{0±128}{2} when ± is plus. Divide 128 by 2.

$$x=64$$

Now solve the equation x=\frac{0±128}{2} when ± is minus. Divide -128 by 2.

$$x=-64$$

The equation is now solved.

$$x=64 x=-64$$