Solve 5a^2=45

$$5 a ^ { 2 } = 45$$

Solve for a

$$a=3$$

$$a=-3$$

Steps Using Difference of Squares

Divide both sides by 5.

$$a^{2}=\frac{45}{5}$$

Divide 45 by 5 to get 9.

$$a^{2}=9$$

Subtract 9 from both sides.

$$a^{2}-9=0$$

Consider a^{2}-9. Rewrite a^{2}-9 as a^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-3\right)\left(a+3\right)=0$$

To find equation solutions, solve a-3=0 and a+3=0.

$$a=3 a=-3$$

Steps by Finding Square Root

Divide both sides by 5.

$$a^{2}=\frac{45}{5}$$

Divide 45 by 5 to get 9.

$$a^{2}=9$$

Take the square root of both sides of the equation.

$$a=3 a=-3$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$a^{2}=\frac{45}{5}$$

Divide 45 by 5 to get 9.

$$a^{2}=9$$

Subtract 9 from both sides.

$$a^{2}-9=0$$

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

$$a=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$a=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$a=\frac{0±6}{2}$$

Now solve the equation a=\frac{0±6}{2} when ± is plus. Divide 6 by 2.

$$a=3$$

Now solve the equation a=\frac{0±6}{2} when ± is minus. Divide -6 by 2.

$$a=-3$$

The equation is now solved.

$$a=3 a=-3$$