Question

Struggling with quadratics - "g(x) = x² + 10x + 9". I'm unsure how to solve this.

Answer 1

To solve the quadratic equation t² + 10t - 200 = 0 using the quadratic formula, follow these steps: identify the values of a, b, and c, substitute the values into the quadratic formula, calculate the discriminant, find the square root of the discriminant, plug the values into the quadratic formula, simplify the expression, and calculate the solutions. The solutions to the quadratic equation t² + 10t - 200 = 0 are t = 10 and t = -20.

Step-by-step explanation:

To solve the quadratic equation t² + 10t - 200 = 0 using the quadratic formula, follow these steps:

1. Identify the values of a, b, and c in the equation:
   a = 1
   b = 10
   c = -200
2. Substitute the values of a, b, and c into the quadratic formula: t = (-b ± sqrt(b² - 4ac)) / (2a)
3. Calculate the discriminant, b² - 4ac:
   b² - 4ac = (10)² - 4(1)(-200) = 100 - (-800) = 900
4. Find the square root of the discriminant: sqrt(900) = 30
5. Plug the values into the quadratic formula:
   t = (-10 ± 30) / 2(1)
6. Simplify the expression:
   t = (-10 + 30) / 2 or t = (-10 - 30) / 2
7. Calculate both solutions:
   t = 20 / 2 or t = -40 / 2
8. Simplify the solutions:
   t = 10 or t = -20

Therefore, the solutions to the quadratic equation t² + 10t - 200 = 0 are t = 10 and t = -20.