Answer:
(x - 5)^2 = 15 and (x + 13)^2 = 3
Explanation:
Sure, I can help you with that.
Let's start with the first equation:
0 = x^2 - 10x + 10
To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.
First, let's factor out the coefficient of x^2:
0 = 1(x^2 - 10x + 10)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:
0 = 1(x^2 - 10x + 25 - 25 + 10)
Now we can rearrange the terms inside the parentheses and simplify:
0 = 1((x - 5)^2 - 15)
Finally, we can rewrite the equation in the desired form by adding 15 to both sides:
15 = (x - 5)^2
So the first equation in the form (x - p)^2 = q is:
(x - 5)^2 = 15
Now let's move on to the second equation:
x^2 + 26x + 167.5 = 0
Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.
First, let's factor out the coefficient of x^2:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)
Now we can rearrange the terms inside the parentheses and simplify:
x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)
Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:
1.5 = (x + 13)^2 - 1.5
So the second equation in the form (x - p)^2 = q is:
(x + 13)^2 = 3