Final answer:
To simplify the expression, combine like terms to get 7t + 2. To use the quadratic formula for solving t² + 10t - 200 = 0, identify the coefficients and substitute them into the formula to find the two values for t.
Step-by-step explanation:
Simplifying the Expression
To simplify the expression t + 2 + 6t, you combine like terms. Both t and 6t are like terms because they both have the variable t to the first power. When you combine t (which is the same as 1t) with 6t, you get 7t. Then, add the constant 2 to obtain the simplified expression: 7t + 2.
Using the Quadratic Formula
To use the quadratic formula to solve for t in the equation t² + 10t - 200 = 0, you first identify the coefficients as a = 1, b = 10, and c = -200. The quadratic formula is t = (-b ± √(b² - 4ac)) / (2a). Substituting the coefficients into the formula gives:
t = (-(10) ± √((10)² - 4(1)(-200))) / (2(1))
Solving this will give you the two possible values for t.