How can I solve for t using the complete the square method?

[jazduck]

I have an equation which I ended up with as t^2 + t = 5.1

How do I then solve for t (without just plugging it into solve on the calculator)?

 

[Cyosis]

This should be in the homework section. You can solve it by using the ABC-formula.

 

[jazduck]

Cyosis - The question is not homework so I put it in general math. The actual question I'm trying is one on the initial velocity of an object required to catch another object released a second before it over a 50m displacement. Not that hard if I make my calculator solve it, just making a mess of the algebra because I havn't done it in 8 years.

Anyway will look up the ABC rule.

 

[Cyosis]

The solution to an equation of the form $ax^2+bx+c=0$ is given by $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$. To make use of this formula you will have to write $t^2+t=5.1$ as $t^2+t-5.1=0$.

 

[HallsofIvy]

Alternatively, you could "complete the square".

For any number, a,
$$(t- a)^2= t^2- 2at+ a^2$$
You have $t^2+ t= 5.1$ which will match the first two terms of that if 2at= t or a= 1/2. In that case $a^2= 1/4$ so adding 1/4 to both sides of the equation: $t^2+ t+ 1/4= 5.1+ 1/4= 5.1+ .25= 5.35$

Now that the left side is a "perfect square" you have $(t+ 1/2)^2= 5.35$ and you can solve that by taking the square root of both sides (remembering that the result can be either positive or negative).