What are the solutions of the equation: x^2 + 14x = -130 ?
a) 2, -16
b) 10, -13
c) -2, 16
d) no solution (~~ MY ANSWER d. ~~)
correct
Yay! Thanks!
A rocket is launched from atop a 105-foot cliff with an initial velocity of 156ft/s. the height of the rocket above the ground at time t is given by
h= -16t^2 + 156t + 105. When will the
rocket hit the ground after it is launched? Round to the nearest second.
(My answer is 10.4 s ??)
To find the solutions of the equation x^2 + 14x = -130, we can start by rearranging the equation to the form of a quadratic:
x^2 + 14x + 130 = 0
This is a quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 14, and c = 130.
To solve the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 14, and c = 130. Plugging these values into the quadratic formula, we have:
x = (-14 ± √(14^2 - 4(1)(130))) / (2(1))
Simplifying further:
x = (-14 ± √(196 - 520)) / 2
x = (-14 ± √(-324)) / 2
Now, since we have a negative value inside the square root, it means that the quadratic equation has no real solutions. This is because the square root of a negative number is not a real number.
Therefore, the correct answer is d) no solution.
LOL
no need to ask, plug back in
h = -16(10.4)^2 + 156(10.4) +105
= -1730.56 + 1622.4 + 105
= -1730.56 + 1727.4
close enough to the ground :)