by completing the square, what value should you add to each side of the equation?
x^2- 7x=5
take 1/2 of the -7 and square that
so (-7/2)^2 = 49/4
we should add 49/4 to both sides
Solve the following and tell how many equations they have:
3(x+2) = 15
x=
How many solutions?
Solve the following and tell how many equations they have:
3(x+2) = 15
To complete the square for the equation x^2-7x=5, you need to add a specific value to each side of the equation to make it a perfect square trinomial.
First, let's rearrange the equation to isolate the terms with x on one side:
x^2 - 7x = 5
To complete the square, you need to take half of the coefficient of the x-term and square it. The coefficient of the x-term is -7, so half of it is -7/2, and when squared we get (49/4).
To maintain the balance of the equation, we need to add (49/4) to both sides. This is the value that you should add to each side of the equation:
x^2 - 7x + 49/4 = 5 + 49/4
On the left side, we have a perfect square trinomial which can be factored as (x - (7/2))^2:
(x - (7/2))^2 = 5 + 49/4
And simplifying the right side:
(x - (7/2))^2 = 20/4 + 49/4
(x - (7/2))^2 = 69/4
Now we have a perfect square trinomial equal to a constant. To solve for x, we can take the square root of both sides:
√((x - (7/2))^2) = √(69/4)
x - (7/2) = ±√(69/4)
Finally, to isolate x, we can add (7/2) to both sides:
x = (7/2) ± √(69/4)
So, by completing the square, you should add (49/4) to each side of the equation x^2 - 7x = 5.