Skip to main content
Solve for t
Tick mark Image

Similar Problems from Web Search

Share

t^{2}-16=0
Divide both sides by 5.
\left(t-4\right)\left(t+4\right)=0
Consider t^{2}-16. Rewrite t^{2}-16 as t^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
t=4 t=-4
To find equation solutions, solve t-4=0 and t+4=0.
5t^{2}=80
Add 80 to both sides. Anything plus zero gives itself.
t^{2}=\frac{80}{5}
Divide both sides by 5.
t^{2}=16
Divide 80 by 5 to get 16.
t=4 t=-4
Take the square root of both sides of the equation.
5t^{2}-80=0
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=\frac{0±\sqrt{0^{2}-4\times 5\left(-80\right)}}{2\times 5}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
t=\frac{0±\sqrt{-4\times 5\left(-80\right)}}{2\times 5}
Square 0.
t=\frac{0±\sqrt{-20\left(-80\right)}}{2\times 5}
Multiply -4 times 5.
t=\frac{0±\sqrt{1600}}{2\times 5}
Multiply -20 times -80.
t=\frac{0±40}{2\times 5}
Take the square root of 1600.
t=\frac{0±40}{10}
Multiply 2 times 5.
t=4
Now solve the equation t=\frac{0±40}{10} when ± is plus. Divide 40 by 10.
t=-4
Now solve the equation t=\frac{0±40}{10} when ± is minus. Divide -40 by 10.
t=4 t=-4
The equation is now solved.