Question

Solve x2 - 16x + 60 = -12 by completing the steps. First, subtract 60 from each side of the equation. Next, add to each side of the equation to complete the square.

Answer 1

The answer is NO SOLUTION

Explanation:

Firstly, we have to subtract 60 from each side of the equation:

`x^2-16*x+60=-12\\x^2-16*x+60-60=-12-60\\x^2-16*x=-72`

Then, to complete a square of a binomial, the rules are:

Let
`(a+b)^2` a square of a binomial, its expansion is:

1. square of the first term
   `a^2`
2. twice the product of the two terms
   `2*a*b`
3. square of the last term
   `b^2`

So,
`(a+b)^2=a^2+2*a*b+b^2`

Then , we have the first term that is
`x` and the second term is
`-8` because
`2*(x)*(-8)=-16*x`.

Therefore, we need to add 64 (=
`(-8)^2`) from each side of the equation:

`x^2-16*x+64=-72+64\\(x-8)^2=-8\\√((x-8)^2)=√(-8)\\x-8=√(-8)`

Finally, we know that it doesn't exist negative square root in the real number group, so there are not "x" values ​​to solve the equation.