Final answer:
To solve the quadratic equation u(u+11)-10=0, expand it to get u2 + 11u - 10 = 0, and then apply the Quadratic Formula by substituting a = 1, b = 11, and c = -10 to find the two solutions for u. These are the solutions for the quadratic equation using the Quadratic Formula.
Step-by-step explanation:
To solve the quadratic equation u(u+11)-10=0 using the Quadratic Formula, we first need to expand the equation and rearrange it to the form au2 + bu + c = 0. Expanding u times (u+11) gives us u2 + 11u, and subtracting 10 from both sides, we have u2 + 11u - 10 = 0. Here, a = 1, b = 11, and c = -10.
Next, we apply the Quadratic Formula:
u = (-b ± √(b2 - 4ac)) / (2a)
Plugging the values into the formula, we get:
u = (-11 ± √((112) - 4(1)(-10))) / (2(1))
u = (-11 ± √(121 + 40)) / 2
u = (-11 ± √161) / 2
This results in two possible solutions for u, which are:
u = (-11 + √161) / 2 and u = (-11 - √161) / 2
These are the solutions for the quadratic equation using the Quadratic Formula.