Final answer:
The term to complete the statement '9t+63=1(t+7)' is not missing; it is a straightforward linear equation that can be simplified to find t = -7. Meanwhile, solving the quadratic equation 't² + 10t - 200 = 0' can be achieved by using the quadratic formula with a=1, b=10, and c=-200.
Step-by-step explanation:
To complete the statement 9t+63=1(t+7), we need to simplify the expression. However, it seems like there might be a typo in the question since 1(t+7) is already simplified and equal to 1t+7. There isn't a term missing in this expression; instead, this is a linear equation that can be simplified as follows:9t + 63 = 1t + 7Let's simplify and solve for t by subtracting 1t from both sides:8t + 63 = 7Now, subtract 63 from both sides to isolate the term with t:8t = -56
Finally, divide by 8 to solve for t:t = -7 In the given quadratic equation t² + 10t - 200 = 0, to solve for t using the quadratic formula, you need to identify the coefficients (a=1, b=10, c=-200) and apply the formula:
t = (-b ± √(b²-4ac)) / (2a)Substitute the coefficients into the formula to find the solutions for t.To eliminate terms and simplify the algebra, follow algebraic principles and operations to reduce the equation to its simplest form. After solving, check the answer to ensure it is reasonable by plugging it back into the original equation.