Question

If, x2 – 49 = (x+a) (x – a), what is the value of a?

Answer 1

a = 7, −7

Step-by-step explanation:

1. Rewrite the equation
2. Simplify
3. Move all terms not containing a to the right side of the equation.
4. Multiply each term in by −1
5. Take the square root of both sides of the equation to eliminate the exponent on the left side.
6. The solution is the result of both the positive and negative portions of the solution.

Answer 2

a = 7 & a = −7

Explanation:

Rewrite the equation as (x+a)(x−a)=x^2−49

Simplify (x+a)(x−a)

x^2−a^2=x^2−49

Move all terms not containing a to the right side of the equation.

−a^2=−49

Multiply each term in −a^2=−49 by −1

a^2=49

Take the square root of both sides of the equation to eliminate the exponent on the left side.

a = ±√49

The complete solution is the result of both the positive and negative portions of the solution.

a = 7,−7