Question

Which equation has the same solution as x^2-12x+12=-3these are the options(x+6)^2=-51(x-6)^2=-51(x+6)^2=21(x-6)^2=21

Answer 1

Second-degree Equation

The second-degree equation is graphically represented as a curve called a parabola.

The parabola can be described by its vertex and leading coefficient as follows:

`y=a(x-h)^2+k`

It's recognized the vertex form of the parabola needs to be expressed as the square of a binomial.

We are given the equation:

`x^2-12x+12=-3`

We need to complete squares to express the equation in vertex form.

Separate the variable terms from the constant terms:

`x^2-12x=-12-3`

Now we complete squares on the left side of the equation. We use the following algebraic identity:

`a^2-2ab+b^2=(a-b)^2`

It's evident that the second term of our equation has a value of b = 12/2=6

Thus, we need to complete squares by adding 6 squared = 36 as follows:

`x^2-12x+36=-12-3+36=21`

Applying the above identity:

`(x-6)^2=21`

Since this equation is a different expression of the very same original equation, they have both the same solution.

Answer: The last choice (x-6)^2=21