# How does this math problem have two answers? x^2-81=-17

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#### Explanation

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Noah G Share
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 $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$. This is called the *difference of squares * identity. Therefore, we can rewrite the equation as

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

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:

Hopefully this helps!

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
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

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

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.

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