Solve the equation for all real solutions in simplest form.t, squared, minus, 5, t, minus, 5, equals, minus, 2, tt 2 −5t−5=−2t

The equation you provided seems to be written in a confusing way. However, I believe you're trying to solve the quadratic equation t^2 - 5t - 5 = -2t.

Let's solve it step by step:

1. First, we need to bring all terms to one side of the equation. We can add 2t to both sides to get this:

   t^2 - 5t + 2t - 5 = 0

2. Simplify the equation:

   t^2 - 3t - 5 = 0

3. Now, we need to solve this quadratic equation. We can use the quadratic formula, which is:

   t = [-b ± sqrt(b^2 - 4ac)] / (2a)

   In our equation, a = 1, b = -3, and c = -5.

4. Substitute a, b, and c into the formula:

   t = [3 ± sqrt((-3)^2 - 41(-5))] / (2*1) t = [3 ± sqrt(9 + 20)] / 2 t = [3 ± sqrt(29)] / 2

So, the solutions to the equation are t = [3 + sqrt(29)] / 2 and t = [3 - sqrt(29)] / 2.