8.1 Completing the Square
To solve the following equation by completing the square, add __________ to both sides.
x^2+6x=10
9
The quadratic formula.
x=(-b+-sqrt(b^2-4ac))/2
Solve:
x-2sqrt(x)=8
16
The classic 1877 novel "Black Beauty" is about what kind of animal?
Horse
Solve using square roots:
(y-3)^2=4
y=5, 1
The discriminant formula.
b^2-4ac
Solve:
3/x+4/(x+2)=1
(3+-sqrt(57))/2
When was the first iPod released?
2001
Solve using square roots:
(z-6)^2=18
6+-3sqrt(2)
What does the discriminant tell us? Be specific, there are three parts to the answer.
If it is less than or equal 1, there are two complex, but not real solutions. If it is equal to 0, there is one real solution. If it is greater or equal to 1, there are two real solutions.
Solve:
4x^4+11x^2=3
x=+-1/2, +-isqrt(3)
What U.S. state grows coffee beans?
Hawaii
Solve by completing the square:
x^2-7x-1=0
Note: you must show steps.
(7+-sqrt(53))/2
Solve:
5x^2-3=14x
3, -1/5
Solve:
(5n+1)^2+2(5n+1)-3=0
x=0 , -4/5
What year was the original “Jurassic Park” released?
1993
Solve by completing the square:
2x^2-3x-5=0
Note, you must show steps.
x=-1, 5/2
A pebble is thrown up into the air from the top of an 1100 foot waterfall. The height, h, of the pebble after t seconds is given by the equation
h=-16t^2+20t+1100
How long after it is thrown will the pebble be 550 feet from the ground? Round to the nearest tenth.
t=6.5 seconds.
Solve:
2x^(2/3)-5x^(1/3)=3
x =-1/8, 27
What is the smallest perfect number? Note: A perfect number is a number which is equal to the sum of its positive divisors or factors excluding itself. Ex. 8128 = 1*8128, 2*4064, 4*2032, 8*1016, 16*508, 32*254, 64*127 and 8128= 1+2+4+8+16+32+64+127+254+508+1016+2032+4064.
6