Answer:
x = 7, x = -7
Step-by-step explanation:
Hi there!
We are given the following equation:
x²-49=0
And we want to solve it for x
x²-49 is actually written in the difference of squares formula, which is a²-b²=(a+b)(a-b)
In this case, x² and 49 represent a² and b², so we'll need to find a and b
For x², we need to find which number or variable multiplies itself to equal x²; in this case, it will be x (x*x=x²)
For 49, we need to find which number multiplies itself to equal 49; in this case, it will be 7 (7 * 7 = 49)
Thus, a in this case is x, and b is 7
Now substitute these values into the formula.
(a+b)(a-b)= (x+7)(x-7)
Now set (x+7)(x-7) (which is x²-49, just expanded out) equal to 0
(x+7)(x-7)=0
Now using zero product property, split and solve:
x+7=0
subtract 7 from both sides
x=-7
x-7=0
Add 7 to both sides
x=7
Therefore, the answer is x = 7, x = -7 (there are 2 answers here that work!)
Hope this helps!
See more on the difference of squares here: https://brainly.com/question/1414397
