Solve 25z^2-9=0

$$25 z ^ { 2 } - 9 = 0$$

Solve for z

$$z=\frac{3}{5}=0.6$$

$$z=-\frac{3}{5}=-0.6$$

Steps Using Difference of Squares

Consider 25z^{2}-9. Rewrite 25z^{2}-9 as \left(5z\right)^{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).

$$\left(5z-3\right)\left(5z+3\right)=0$$

To find equation solutions, solve 5z-3=0 and 5z+3=0.

$$z=\frac{3}{5} z=-\frac{3}{5}$$

Steps by Finding Square Root

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

$$25z^{2}=9$$

Divide both sides by 25.

$$z^{2}=\frac{9}{25}$$

Take the square root of both sides of the equation.

$$z=\frac{3}{5} z=-\frac{3}{5}$$

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.

$$25z^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 25\left(-9\right)}}{2\times 25}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 25\left(-9\right)}}{2\times 25}$$

Multiply -4 times 25.

$$z=\frac{0±\sqrt{-100\left(-9\right)}}{2\times 25}$$

Multiply -100 times -9.

$$z=\frac{0±\sqrt{900}}{2\times 25}$$

Take the square root of 900.

$$z=\frac{0±30}{2\times 25}$$

Multiply 2 times 25.

$$z=\frac{0±30}{50}$$

Now solve the equation z=\frac{0±30}{50} when ± is plus. Reduce the fraction \frac{30}{50} to lowest terms by extracting and canceling out 10.

$$z=\frac{3}{5}$$

Now solve the equation z=\frac{0±30}{50} when ± is minus. Reduce the fraction \frac{-30}{50} to lowest terms by extracting and canceling out 10.

$$z=-\frac{3}{5}$$

The equation is now solved.

$$z=\frac{3}{5} z=-\frac{3}{5}$$