Solve X^2-49=0

$$X ^ { 2 } - 49 = 0$$

Solve for X

$$X=7$$

$$X=-7$$

Steps Using Difference of Squares

Consider X^{2}-49. Rewrite X^{2}-49 as X^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(X-7\right)\left(X+7\right)=0$$

To find equation solutions, solve X-7=0 and X+7=0.

$$X=7 X=-7$$

Steps by Finding Square Root

Add 49 to both sides. Anything plus zero gives itself.

$$X^{2}=49$$

Take the square root of both sides of the equation.

$$X=7 X=-7$$

Steps Using the Quadratic Formula

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.

$$X^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$X=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

Square 0.

$$X=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

Multiply -4 times -49.

$$X=\frac{0±\sqrt{196}}{2}$$

Take the square root of 196.

$$X=\frac{0±14}{2}$$

Now solve the equation X=\frac{0±14}{2} when ± is plus. Divide 14 by 2.

$$X=7$$

Now solve the equation X=\frac{0±14}{2} when ± is minus. Divide -14 by 2.

$$X=-7$$

The equation is now solved.

$$X=7 X=-7$$