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Solve x2 − 8x + 5 = 0 using the completing-the-square method.

x = negative four plus or minus the square root of eleven

x = four plus or minus the square root of eleven

x = negative four plus or minus the square root of five

x = four plus or minus the square root of five

Verified Answer :

Answer:

Option 2

Step-by-step explanation:

We have been given a quadratic equation \(x^2-8x+5=0\)

First step in completing method square is to make the coefiicient of  \(x^2\)  1

Since, in given quadratic equation coefficient of \(x^2\) is already 1. we will proceed to the next step which is add and subtract square of the half of coefficient of x in given quadratic equation.

Here, half of coefficient of x that is  8 would be 4 so we will add and subtract \(4^2\) in given quadratic equation we will get

\(x^2-8x+4^2-4^2+5=0\)  

Now, we will proceed to the third step that is making the whole square formula according to the terms

Here, we can see that we are geeting the formula of \((x-4)^2\) from \(x^2-8x+4^2\)

The equation will become \((x-4)^2-4^2+5=0\)

After simplifying we will get  \((x-4)^2-16+5=0\)

After further simplification we will get \((x-4)^2-11=0\)

After more simplification we will get \((x-4)=\pm\sqrt{11}\)

Hence, we will get the value of x which is \(x=4\pm\sqrt{11}\)

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