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

Answer:

The answer is NO SOLUTION

Step-by-step 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:

$x^2-16*x+64=-72+64\\(x-8)^2=-8\\\sqrt{(x-8)^2}=\sqrt{-8}\\x-8=\sqrt{-8}$

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.

Answer 2

x^2 - 16x + 60 = -12

Step 1):

x^2 - 16x = -72

Step 2) Add 64 to both sides

x^2 - 16x + 64 = -8

Then factor:

(x-8)^2 = -8

Square root both sides:

x - 8 = sqrt(-8)

You cannot take the square root of a negative number.  Thus, this equation has NO SOLUTION.