So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19
I'm going to assume the given equation equals zero..
So, If we add subtract 19 from both sides of the equation we get the perfect square.
4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0
for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)
Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.
To find the lowest common denominator you need to know the factors of 5 and 11.
So make two lists:
5, 10, 15, 20, 25, 30, and so on.
11, 22, 33, 44, 55, 66, and so on.
Keep doing that until you find the lowest common number in the lists. The LCD will be 55.
Answer:
Step-by-step explanation:
3x + 3y = -3 given
3x = -3y - 3 subtract 3y from both sides
x = -y -1 divide everything by 3
hope this helps <3
Answer:
radius = 7 units
Step-by-step explanation:
Given:
Radius = 7 units
Find area of 4 circles:
1 circle = π (7)² = 49π units²
4 circles = 49π x 4 = 196π units²
Find radius of sphere:
4πr² = 196π
r² = 49
r = 7
