Form the perfect square trinomial in the process of completing the square. What is the value of c?
x^2 + 3x + c = 7/4 + c
c =
Take 1/2 of the middle term and square it to find c.
3/2 squared = 9/4 = c
When you factor
(x +3/2)(x + 3/2)
check: x^2 + 3/2 x + 3/2 x + 9/4
x^2 + 6/2 x + 9/4
x^2 + 3x + 9/4
Thanks!!! <3
To complete the square, we want to rewrite the trinomial in the form of (x + a)^2, where 'a' is a constant.
Given the equation x^2 + 3x + c = 7/4 + c, we want to rewrite the left side of the equation as a perfect square trinomial.
To do this, we take half of the coefficient of x (which is 3), square it (which is 9), and add it to both sides of the equation:
x^2 + 3x + 9 + c = 7/4 + c + 9
Simplifying the equation gives:
(x + 3/2)^2 + c = (28 + 4c)/4
Now, we can compare the two sides of the equation to identify the value of 'c'.
From the equation, it is clear that c = (28 + 4c)/4.
To solve the equation, we can multiply both sides by 4 to get rid of the denominator:
4c = 28 + 4c
Subtracting 4c from both sides gives:
0 = 28
However, we reached an inconsistency, as 0 cannot be equal to 28. Therefore, there is no value of 'c' that satisfies the equation x^2 + 3x + c = 7/4 + c.
To form a perfect square trinomial, we need to take the coefficient of x, divide it by 2, and square the result.
In this case, the coefficient of x is 3, so we divide it by 2: 3/2 = 1.5.
Then square the result: 1.5^2 = 2.25.
Therefore, the value of c is 2.25.