The number of real solutions of the equation $x^2 - 10|x| - 56 = 0$ is

There are two cases when we open the modulus:

I. Positive Sign (assumption: $x>0$)

$x^2 - 10|x| - 56 = 0$

$x^2 - 10x - 56 = 0$

$x = 14, -4$

Note: Become smart in finding the values of $x$ without writing all the steps (you find the two numbers to split the middle term, reverse the signs).

Since our assumption was $x>0$, then only $x=14$ is the accepted value.

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II. Negative Sign (assumption: $x<0$)

$x^2 - 10|x| - 56 = 0$

$x^2 + 10x - 56 = 0$

$x = -14, 4$

Since our assumption was $x<0$, then only $x=-14$ is the accepted value.

Thus, there are only 2 solutions.

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