Final answer:
To solve the equation 13t^2 - 8t + 1 = -3t^2 using the quadratic formula, rearrange the equation to ax^2 + bx + c = 0 and then substitute the values into the formula t = (-b ± √(b^2 - 4ac)) / (2a).
Step-by-step explanation:
To solve the quadratic equation 13t^2 - 8t + 1 = -3t^2 using the quadratic formula, we need to rearrange the equation so that it is in the form ax^2 + bx + c = 0:
16t^2 - 8t + 1 = 0
Comparing this to the quadratic equation form, we have a = 16, b = -8, and c = 1. Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
t = (-(-8) ± √((-8)^2 - 4(16)(1))) / (2(16))
t = (8 ± √(64 - 64)) / 32
t = (8 ± √0) / 32
t = (8 ± 0) / 32
t = 8/32
t = 1/4