Question

Consider the equation:
\[0=x^2-10x+10\]
1) Rewrite the equation by completing the square.
Your equation should look like
\[(x+a)^2=b\] or
\[(x-c)^2=d\].
2) What are the solutions to the equation?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[x = -5 \pm \sqrt{15}\]
A
\[x = -5 \pm \sqrt{15}\]
(Choice B)
\[x = 5 \pm \sqrt{15}\]
B
\[x = 5 \pm \sqrt{15}\]
(Choice C)
\[x = -15 \pm \sqrt{5}\]
C
\[x = -15 \pm \sqrt{5}\]
(Choice D)
\[x = 15 \pm \sqrt{5}\]
D
\[x = 15 \pm \sqrt{5}\]

Answer 1

To solve the given equation \(0 = x^2 - 10x + 10\) by completing the square, we can follow these steps:

### 1) Completing the Square

Start with the equation:

\[
x^2 - 10x + 10 = 0
\]

First, we isolate the constant term on the right:

\[
x^2 - 10x = -10
\]

Next, we complete the square on the left side. To do this, take half of the coefficient of \(x\), which is \(-10\), and square it. Half of \(-10\) is \(-5\), and squaring it gives \(25\):

\[
x^2 - 10x + 25 = -10 + 25
\]

This simplifies to:

\[
(x - 5)^2 = 15
\]

Now, we have the equation in the completed square form:

\[
(x - 5)^2 = 15
\]

### 2) Finding the Solutions

Now, we solve for \(x\) by taking the square root of both sides:

\[
x - 5 = \pm \sqrt{15}
\]

This gives us two solutions:

\[
x = 5 + \sqrt{15}
\]
\[
x = 5 - \sqrt{15}
\]

Thus, the solutions can be expressed as:

\[
x = 5 \pm \sqrt{15}
\]

### Conclusion

The correct answer is:

**(Choice B)**
\[x = 5 \pm \sqrt{15}\]