Question

Complete the process of solving the equation. Fill in the missing term on each line. Simplify any fractions.

2(t+2)=14
t+2= Divide both sides by 2
t= Subtract 2 from both sides

Answer 1

To solve the equation t² + 10t - 2000 = 0 using the quadratic formula, rearrange the equation and substitute the values of a, b, and c into the formula. Simplify the equation and find the two solutions.

Step-by-step explanation:

To solve the equation t² + 10t - 2000 = 0 using the quadratic formula, we need to rearrange the equation so that it is in the form ax² + bx + c = 0. In this case, a = 1, b = 10, and c = -2000. The quadratic formula is given by:

t = (-b ± √(b² - 4ac)) / (2a)

Substituting the values of a, b, and c into the formula, we get:

t = (-10 ± √(10² - 4(1)(-2000))) / (2(1))

Simplifying, we have:

t = (-10 ± √(100 + 8000)) / 2

t = (-10 ± √8100) / 2

t = (-10 ± 90) / 2

We have two solutions:

t = (-10 + 90) / 2 = 40 / 2 = 20

and

t = (-10 - 90) / 2 = -100 / 2 = -50