<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
Answer:
.66
Step-by-step explanation:
cmon bro how do u not know this
4 divide 6
.66666666666666666666666666666666666
Answer:
The answer is 2(the square root of 65 )
Step-by-step explanation:
Plug ( -6, 2) and (8, 10) into the distance formula and solve.
Distance = the square root of ((x2 - x1)^2 + (y2 - y1)^2))
Distance = the square root of ((8 - -6)^2 + (10 - 2)^2))
Distance = the square root of (14^2 + 8^2)
Distance = the square root of (196 + 64)
Distance = the square root of 260 which can be simplified to 2(the square root of 64)
Answer:
I believe the answer is C
Step-by-step explanation:
Answer:
1,500 points per minute
Step-by-step explanation:
You can tell it's 1500 points per minute because the lines meet up at (2,3) meaning that 3/2 = 1500, to double check you could do 9/6 where the points also meet up at the exit of the graph which is ALSO 1.5 meaning 1,500 points per minute
