Chapter 9, Problem 23MCQ

To determine

To solve the given equation by factoring.

Answer to Problem 23MCQ

The value of x is -6 and 8 .

Explanation of Solution

Given information :

The equation provided is $x^2-2x=48$ . This can be written as $x^2-2x-48=0$ .

Formula used :

The given equation can be solved by factoring. To do so, break up the midpoint to arrive at two factors. Then use the zero-product property to equate each factor in order to get the roots.

Calculation :

  $x^2-2x-48=0$

Given equation.

  $=>x^2-8x+6x-48=0$

Breaking the middle term.

  $=>x\left(x-8\right)+6\left(x-8\right)=0$

Arranging the common factors.

  $=>\left(x+6\right)\left(x-8\right)=0$

The two factors of the function.

Now, the first root is:

  $x+6=0$

Using zero-product property.

  $x=-6$

The second root is:

  $x-8=0$

Using zero-product property.

  $x=8$

Thus, the values of x are -6 and 8 .