Solve g^2-9=0

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

Solve for g

$$g=3$$

$$g=-3$$

Steps Using Difference of Squares

Consider g^{2}-9. Rewrite g^{2}-9 as g^{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).

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

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

$$g=3 g=-3$$

Steps by Finding Square Root

Add 9 to both sides. Anything plus zero gives itself.

$$g^{2}=9$$

Take the square root of both sides of the equation.

$$g=3 g=-3$$

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.

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

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}.

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

Square 0.

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

Multiply -4 times -9.

$$g=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$g=\frac{0±6}{2}$$

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

$$g=3$$

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

$$g=-3$$

The equation is now solved.

$$g=3 g=-3$$