Solve t^2-25=0

$$t ^ { 2 } - 25 = 0$$

Solve for t

$$t=5$$

$$t=-5$$

Steps Using Difference of Squares

Consider t^{2}-25. Rewrite t^{2}-25 as t^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(t-5\right)\left(t+5\right)=0$$

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

$$t=5 t=-5$$

Steps by Finding Square Root

Add 25 to both sides. Anything plus zero gives itself.

$$t^{2}=25$$

Take the square root of both sides of the equation.

$$t=5 t=-5$$

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.

$$t^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -25.

$$t=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$t=\frac{0±10}{2}$$

Now solve the equation t=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$t=5$$

Now solve the equation t=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$t=-5$$

The equation is now solved.

$$t=5 t=-5$$