Solve a^2=49

$$a ^ { 2 } = 49$$

Solve for a

$$a=7$$

$$a=-7$$

Steps Using Difference of Squares

Subtract 49 from both sides.

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

Consider a^{2}-49. Rewrite a^{2}-49 as a^{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).

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

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

$$a=7 a=-7$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$a=7 a=-7$$

Steps Using the Quadratic Formula

Subtract 49 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -49.

$$a=\frac{0±\sqrt{196}}{2}$$

Take the square root of 196.

$$a=\frac{0±14}{2}$$

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

$$a=7$$

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

$$a=-7$$

The equation is now solved.

$$a=7 a=-7$$