Question

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

Answer 1

a is 7

Step-by-step explanation:

x²-49

so you are finding the difference of squares

and if you look closely, you can see that the equation has squares.

49 has the square root of 7, but the rules on squares state that the squared number comes in both positive and negative numbers.

so a is equal to both -7 and +7

PS i hope this helps

Answer 2

a = 7 & a = −7

Step-by-step 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