what value of k makes the given expression a perfect square?M square -8m+k
my question is what is the value of k that makes the given expression a perfect square 2m²-8m+k
m^2 - 8 m + k
(m-x)(m-x) = m^2 -2 x m + x^2
so
2 x = -8
x = -4
x^2 = 16 = k
so
m^2 - 8 m + 16
in general to complete the square
1 x^2 + b x + c
if that is to be a perfect square
c = (b/2)^2
Haha, I see you're trying to find value of k to make the expression a perfect square. Well, let's solve this puzzle!
To make the expression a perfect square, we need to find a value of k that completes the square. In this case, the expression is M^2 - 8M + k.
To complete the square, we can take half of the coefficient of M and square it. In this case, half of 8 is 4, and 4 squared is 16. So, to make the expression a perfect square, k should be equal to 16.
Therefore, the value of k that makes the given expression a perfect square is 16. Ta-da! 🎉
To determine the value of k that makes the expression a perfect square, we need to complete the square.
We have the expression: M^2 - 8M + k.
To complete the square, we need to take half of the coefficient of M, square it, and add it to both sides of the equation.
The coefficient of M is -8, so half of -8 is -4, and (-4)^2 is 16.
Let's add 16 to both sides of the equation:
M^2 - 8M + 16 + k = M^2 - 8M + 16
Now, the left side of the equation is a perfect square trinomial. It can be factored as the square of a binomial:
(M - 4)^2 = M^2 - 8M + 16
Therefore, to make the original expression a perfect square, the value of k should be 16.
To find the value of k that makes the expression a perfect square, we need to complete the square.
Step 1: Start with the given expression: M^2 - 8M + k.
Step 2: Take half of the coefficient of the middle term (-8M) and square it. Here, half of -8M is -4M, and (-4M)^2 is 16M^2.
Step 3: Add the square we found in step 2 to the expression. The expression becomes: M^2 - 8M + 16M^2 + k.
Step 4: Simplify the expression. We can combine like terms: (1 + 16)M^2 - 8M + k, which simplifies to 17M^2 - 8M + k.
At this point, the expression is now a perfect square trinomial since it can be factored into a square of a binomial. So, the value of k that makes the expression a perfect square is equal to half the coefficient of the middle term (8M) squared, which is (8M/2)^2 = 16M^2.
Therefore, k = 16M^2.
In summary, the value of k that makes the expression M^2 - 8M + k a perfect square is k = 16M^2.