If x^2 +17 = 81, what is the value of x?

2 Answers
Feb 9, 2018

The highest power is 2.

Explanation:

Because x has a maximum power of 2, there will be 2 answers. if it were 3, there could be up to 3 answers, etc.

While solving this problem, you gather all terms on one side so the equation looks like

x^2-81+17=0

x^2-64=0

then factor

(x-8)(x+8) = 0

then, because any number times 0 equals 0, we know that one of the two parts in the parenthesis must be equal to 0, so

x-8=0 or x+8=0

and so the two answers x=8,-8 come to be.

Feb 9, 2018

We start by putting all terms to one side of the equal sign:

x^2 - 81 + 17 = 0

x^2 - 64= 0

Note that (a- b)(a + b) = a^2 - b^2. This is called the *difference of squares * identity. Therefore, we can rewrite the equation as

(x + 8)(x - 8) = 0

We can now see that if x= +8 or x= -8, the equation will hold true.

We can also confirm graphically. If we trace the parabola y_1 = x^2 - 64, the x-intercepts will be the solution to 0 = x^2 -64. Let's check:

enter image source here

Therefore, our answer is correct.

Hopefully this helps!