Question

Write x2 - 8x + 13 = 0 in the form (x - a)2 = b, where a and b are integers.

Answer 1

The question is asking to write x^2-8x+13 in the form of (x-1)2 = b where as a and b are integers, base on the said formula, I would say that the correct answer would be (x - 4)2 = 3, I hope you are satisfied with my answer and feel free to ask for more if you have questions and further clarifications 

Answer 2

Answer:

A) $(x - 4)^2 = 3$

Step-by-step explanation:

The given equation is $x^{2} -8x +13 = 0$

We have to convert this quadratic equation in the form of $(x -a)^{2} = b$.

Here we have to use the completing square method.

Identify the value of b from the given quadratic equation.

b = -8 now divide it by 2 and square it.

$(\frac{b}{2})^{2}$

= $(\frac{-8}{2} )^2$

= $(-4)^{2}$

= 16

Now add 16 on both side of the equation

$x^{2} - 8x + 16 + 13 = 16$

$(x^{2} -8x +16) +13 = 16$

Now subtract 13 on both sides, we get

$(x^{2} - 8x +16) + 13 -13 = 16 -13$

$x^{2} -8x + 16 = 3$

Here $(x -4)^{2} = x^2 -8x +16$

So, we get

$(x - 4)^2 = 3$

Therefore, answer is A) $(x - 4)^2 = 3$