Solve 36t^2-25=0

$$36 t ^ { 2 } - 25 = 0$$

Solve for t

$$t=\frac{5}{6}\approx 0.833333333$$

$$t=-\frac{5}{6}\approx -0.833333333$$

Steps Using Difference of Squares

Consider 36t^{2}-25. Rewrite 36t^{2}-25 as \left(6t\right)^{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).

$$\left(6t-5\right)\left(6t+5\right)=0$$

To find equation solutions, solve 6t-5=0 and 6t+5=0.

$$t=\frac{5}{6} t=-\frac{5}{6}$$

Steps by Finding Square Root

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

$$36t^{2}=25$$

Divide both sides by 36.

$$t^{2}=\frac{25}{36}$$

Take the square root of both sides of the equation.

$$t=\frac{5}{6} t=-\frac{5}{6}$$

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.

$$36t^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 36\left(-25\right)}}{2\times 36}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 36\left(-25\right)}}{2\times 36}$$

Multiply -4 times 36.

$$t=\frac{0±\sqrt{-144\left(-25\right)}}{2\times 36}$$

Multiply -144 times -25.

$$t=\frac{0±\sqrt{3600}}{2\times 36}$$

Take the square root of 3600.

$$t=\frac{0±60}{2\times 36}$$

Multiply 2 times 36.

$$t=\frac{0±60}{72}$$

Now solve the equation t=\frac{0±60}{72} when ± is plus. Reduce the fraction \frac{60}{72} to lowest terms by extracting and canceling out 12.

$$t=\frac{5}{6}$$

Now solve the equation t=\frac{0±60}{72} when ± is minus. Reduce the fraction \frac{-60}{72} to lowest terms by extracting and canceling out 12.

$$t=-\frac{5}{6}$$

The equation is now solved.

$$t=\frac{5}{6} t=-\frac{5}{6}$$