Sure, let’s solve the given equation by completing the square step by step.
### Step 1: Move the constant term to the right side
Given the equation:
[tex]\[ 0 = x^2 - 10x + 10 \][/tex]
We can rewrite it as:
[tex]\[ x^2 - 10x + 10 = 0 \][/tex]
### Step 2: Move the constant term to the right side
Rearrange the equation to isolate the x terms:
[tex]\[ x^2 - 10x = -10 \][/tex]
### Step 3: Complete the square
To complete the square, we add and subtract the square of half the coefficient of [tex]\(x\)[/tex]. The coefficient of [tex]\(x\)[/tex] is [tex]\(-10\)[/tex], so half of [tex]\(-10\)[/tex] is [tex]\(-5\)[/tex], and squaring it gives [tex]\((\-5)^2 = 25\)[/tex].
Add and subtract 25 inside the equation:
[tex]\[ x^2 - 10x + 25 - 25 = -10 \][/tex]
[tex]\[ (x - 5)^2 - 25 = -10 \][/tex]
Then, move the [tex]\(-25\)[/tex] to the right side:
[tex]\[ (x - 5)^2 = 15 \][/tex]
Here, we have [tex]\(W = 5\)[/tex] and [tex]\(b = 15\)[/tex].
### Step 4: Solve for [tex]\(x\)[/tex]
The equation [tex]\((x - 5)^2 = 15\)[/tex] can be solved by taking the square root on both sides:
[tex]\[ x - 5 = \pm \sqrt{15} \][/tex]
So, the solutions are:
[tex]\[ x = 5 + \sqrt{15} \][/tex]
[tex]\[ x = 5 - \sqrt{15} \][/tex]
Thus, the solutions to the equation are:
[tex]\[ x = 5 \pm \sqrt{15} \][/tex]
### Step 5: Choose the correct answer
The correct answer from the given options is:
(B) [tex]\(x = 5 \pm \sqrt{15}\)[/tex]
