Question

Solve x2 − 24x = −80 by completing the square.

What is the solution set of the equation?

{2, 40}
{4, 20}
{5, 16}
{8, 10}

Answer 1

Answer:

{4, 20}

Step-by-step explanation:

x2 − 24x = −80

divide -24 by 2  and square result   get 144

x^2 - 24x  + 144 =  -80 + 144

(x - 12)^2  =  64

x - 12 = root (64)

x = 12 + 8  or  x = 12 - 8

x = 20 or 4

Answer 2

The solution set of the considered quadratic equation x^2 − 24x = −80 is given by: Option B: {4,20}

What is completing the squares method for solving the quadratic equations in one variable?

The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.

The quadratic equation would look something like:

(px + q)^2 = s

where p, q and s are some constants.

We do so, so that we can then use square root and some other operations to get the variable 'x' on one side of the equation, and all the constants on the other side, being solution of the considered  quadratic equation.

Expressing the quadratic equation in such form converts the form of the equation which contains 'x' with different powers in different term to a form which contains 'x' single time.

What is the expansion of square of sum of two terms?

Suppose that two terms are 'a' and 'b'.

Then, their sum's square is expanded as:

$(a+b)^2 = a^2 + 2ab + b^2$

For this case, the equation considered is :

$x^2 -24x = -80$

Comparing the left side with $a^2 + 2ab + b^2$, we see that we can use a = x.

Let we try to make the considered equation look more like the equation  $a^2 + 2ab + b^2$ .

$x^2 -24x = -80\\x^2 -2(12)x = -80\\x^2 -2(12)x + 12^2 -12^2 = -80\\x^2 -2(12)x + 12^2 = -80 + 12^2 = 64$

Now, we can use $(a+b)^2 = a^2 + 2ab + b^2$ for the left sided expression, as shown below:

$x^2 -2(12)x + 12^2= 64\\\\(x-12)^2 = 64$

Taking square root, we get:

$\sqrt{(x-12)^2} = \sqrt{64}\\\\(x-12) = \sqrt{(\pm 8)^2} = \pm 8\\or\\\\x = 12 \pm 8\\x = 12+8, x = 12-8\\x = 20, x = 4$

Thus, the solution set of the considered quadratic equation x^2 − 24x = −80 is given by: Option B: {4,20}

Learn more about completing the squares method here:

https://brainly.com/question/16800259

#SPJ2