Solve 9s^2-729=0

$$9 s ^ { 2 } - 729 = 0$$

Solve for s

$$s=9$$

$$s=-9$$

Steps Using Difference of Squares

Divide both sides by 9.

$$s^{2}-81=0$$

Consider s^{2}-81. Rewrite s^{2}-81 as s^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(s-9\right)\left(s+9\right)=0$$

To find equation solutions, solve s-9=0 and s+9=0.

$$s=9 s=-9$$

Steps by Finding Square Root

Add 729 to both sides. Anything plus zero gives itself.

$$9s^{2}=729$$

Divide both sides by 9.

$$s^{2}=\frac{729}{9}$$

Divide 729 by 9 to get 81.

$$s^{2}=81$$

Take the square root of both sides of the equation.

$$s=9 s=-9$$

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.

$$9s^{2}-729=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -729 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\times 9\left(-729\right)}}{2\times 9}$$

Square 0.

$$s=\frac{0±\sqrt{-4\times 9\left(-729\right)}}{2\times 9}$$

Multiply -4 times 9.

$$s=\frac{0±\sqrt{-36\left(-729\right)}}{2\times 9}$$

Multiply -36 times -729.

$$s=\frac{0±\sqrt{26244}}{2\times 9}$$

Take the square root of 26244.

$$s=\frac{0±162}{2\times 9}$$

Multiply 2 times 9.

$$s=\frac{0±162}{18}$$

Now solve the equation s=\frac{0±162}{18} when ± is plus. Divide 162 by 18.

$$s=9$$

Now solve the equation s=\frac{0±162}{18} when ± is minus. Divide -162 by 18.

$$s=-9$$

The equation is now solved.

$$s=9 s=-9$$