To solve for t in this equation, we need to use the quadratic formula. First, we rearrange the equation to t^2 + t - 5.1 = 0. Then, we plug in the values of a=1, b=1, and c=-5.1 into the formula: t = (-1 ± √(1^2 - 4(1)(-5.1))) / 2(1). This results in two solutions: t = 1.9 or t = -2.9.
Yes, we can also use factoring to solve for t. In this case, we would need to find two numbers that multiply to -5.1 and add to 1. Using trial and error, we can find that 5.1 and -1 work, so we can rewrite the equation as (t+5.1)(t-1) = 0. This means that either t+5.1 = 0 or t-1 = 0, resulting in the same solutions as using the quadratic formula.
The solutions to this equation represent the values of t that make the equation true. In other words, when we plug in either t = 1.9 or t = -2.9 into the original equation, it will equal 5.1.
No, since this is a quadratic equation, it can only have at most two solutions. This is because a quadratic equation is a polynomial of degree 2, meaning it has only two terms with variables raised to the power of 2 or less.
To check if our solutions are correct, we can substitute them back into the original equation and see if it equals 5.1. For example, if we check t = 1.9, we get (1.9)^2 + (1.9) = 3.61 + 1.9 = 5.51, which is close to 5.1 but not exactly. This is due to rounding errors from using the quadratic formula. However, if we check t = -2.9, we get (-2.9)^2 + (-2.9) = 8.41 - 2.9 = 5.51, which is also close to 5.1. Therefore, both solutions are correct.