<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>
(x+5,y-6) is the coordinate notation.
A'B'C' is larger than ABC, so the scale factor would be a whole number, scale factor of 2.
A'B'C'is also a morrir image of ABC, notice on ABC A is on the left and B is on the right, but on A'B'C', B" is on the left and A' is on the right.
This means it was reflected across the Y axis.
The first answer is the correct one.
It wouldn't be able to be because since all of the the numbers that could fit is probably going to be a decimal. Let's say we find 4 consecutive numbers of 32.
Equation:
x+(x+1)+(x+2)+(x+3)=32
4x+6=32
-6 -6
4x=26
x=6.5 1. 6.5, 7.5, 8.5, 9.5
As you can see, the consecutive number is going to be a decimal.
Answer:
8 < x < 2 has no solution because there is no number greater than 8 (8 < x), yet less than 2 (x < 2). It's impossible, so there is no solution.
If the inequality was something like 8 < x < 10, then it will work because 8 can be less than x and x can be less than 10.
Hope this helps and have a great rest of your day! :)
