Completing the square has us breaking rules of solving equations and factoring out the greatest common factor, but it is what it is! The first step is to make sure that the coefficient on the x^2 term is a 1 and it is so we are good there. Now subtract 9 from both sides to get x^2 + 16x = -9. Complete the square on the left side by taking half of the linear term (16x) which is 8 and then squaring it to get 64. That's what is added to both sides. Now it looks like this:
x^2 + 16x + 64 = -9 + 64. If you were to write it in vertex form it would look like this: (x+8)^2 - 55 = 0. Now you can use this to plot the vertex of a parabola if you want to: it sits at (-8, -55)
1+1+1+1+1+5+5+5+5 is one
5+5+5+1+1+1+1+1+1+1+1+1+1 is another
5+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 is three
5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 is four.
There are 4 combinations.
Use the power, product, and chain rules:
• product rule
• power rule for the first term, and power/chain rules for the second term:
• power rule
Now simplify.
You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.
On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify
Differentiate both sides and you end up with the same derivative:
The answer is: t = 1
You need to separate t from everything to figure out what it is.
Step 1: Subtract 9 from both sides, so we get 7 - 2t = 5t
Step 2: Add 2t to both sides, so we get 7 = 7t.
Step 3: Divide by 7, meaning t = 1.
Next you should check your work. If we plug 1 in for t, we get 14 = 14, so the answer is correct.
Hope this helps!