Solve X^2-365=364

$$X ^ { 2 } - 365 = 364$$

Solve for X

$$X=27$$

$$X=-27$$

Steps Using Difference of Squares

Subtract 364 from both sides.

$$X^{2}-365-364=0$$

Subtract 364 from -365 to get -729.

$$X^{2}-729=0$$

Consider X^{2}-729. Rewrite X^{2}-729 as X^{2}-27^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(X-27\right)\left(X+27\right)=0$$

To find equation solutions, solve X-27=0 and X+27=0.

$$X=27 X=-27$$

Steps by Finding Square Root

Add 365 to both sides.

$$X^{2}=364+365$$

Add 364 and 365 to get 729.

$$X^{2}=729$$

Take the square root of both sides of the equation.

$$X=27 X=-27$$

Steps Using the Quadratic Formula

Subtract 364 from both sides.

$$X^{2}-365-364=0$$

Subtract 364 from -365 to get -729.

$$X^{2}-729=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -729 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$X=\frac{0±\sqrt{0^{2}-4\left(-729\right)}}{2}$$

Square 0.

$$X=\frac{0±\sqrt{-4\left(-729\right)}}{2}$$

Multiply -4 times -729.

$$X=\frac{0±\sqrt{2916}}{2}$$

Take the square root of 2916.

$$X=\frac{0±54}{2}$$

Now solve the equation X=\frac{0±54}{2} when ± is plus. Divide 54 by 2.

$$X=27$$

Now solve the equation X=\frac{0±54}{2} when ± is minus. Divide -54 by 2.

$$X=-27$$

The equation is now solved.

$$X=27 X=-27$$