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diamong [38]
3 years ago
8

What number would you add to the equation below to complete the square?x2 + 4x = 0?

Mathematics
1 answer:
julia-pushkina [17]3 years ago
7 0
------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0

------------------------------------------------------------------
Add a constant
------------------------------------------------------------------
x² + 4x + (4/2)² - (4/2)²  = 0   ← Add 2² to form perfect square

------------------------------------------------------------------
Evaluate bracket
------------------------------------------------------------------
x² + 4x + 2² - 2² = 0

------------------------------------------------------------------
Form the perfect square
------------------------------------------------------------------
(x + 2)² = 4 

------------------------------------------------------------------
Square root both sides
------------------------------------------------------------------
(x+2) = \pm √4

------------------------------------------------------------------
Evaluate the square root
------------------------------------------------------------------
(x+2) = \pm 2

------------------------------------------------------------------
Solve x 
------------------------------------------------------------------
x = 2 - 2 or x = -2 - 2

x = 0 or -4

------------------------------------------------------------------
Answer: The constant to add is 4 and the value of x = 0 or -4
------------------------------------------------------------------



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Tim x: 3x(x-2) + 2(2-x)=0
olganol [36]

Answer:

Assuming this is the full problem.

3x^2-8x+4

Step-by-step explanation:

6 0
3 years ago
2. Determine the sum of the first 400 ODD numbers.<br><br>​
il63 [147K]

Odd numbers take the form 2n-1, where n\ge1 is an integer. When n=400, the last odd number would be 799. So we're adding

S=1+3+5+\cdots+795+797+799

By reversing the order of terms, we have

S=799+797+795+\cdots+5+3+1

and we can pair up terms in both sums at the same position to write

2S=(1+799)+(3+797)+(5+795)+\cdots(795+5)+(797+3)+(799+1)

so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:

2S=400\cdot800\implies S=160,000

###

We could also make use of the formulas,

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2

We have

S=\displaystyle\sum_{i=1}^{400}(2i-1)=2\sum_{i=1}^{400}i-\sum_{i=1}^{400}1=400(400+1)-400=400^2=160,000

3 0
3 years ago
How do you do this, can someone help please?
igor_vitrenko [27]

Answer:

your answer is C.

Step-by-step explanation:

4 0
3 years ago
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