# Solve for x in each of the following, x E C. x^6-7x^3-8=0

hustoncmk | High School Teacher | (Level 1) Assistant Educator

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You need to begin by first factoring the equation to simplest terms.

In your equation x^6 - 7x^3 - 8 =0, start with the term x^6 this can be x^3 * x^3.  You would then set up two new parentheses and place x^3 as the first term in each (x^3 + ?)(X^3 + ?)= 0

To determine what goes where the question marks are you need to look for factors of -8 that add to -7.

Factors of -8    sum of factors

1, -8                      -7

2, -4                      -2

4, -2                       2

8, -1                      7

From the chart above, you can determine 1, -8.

Your equation is now (x^3 + 1)(x^3 - 8) = 0

You would then set each of these factor equal to zero & solve.

X^3 + 1 = 0                       X^3 - 8 = 0

X^3 = -1                           X^3  = 8

x = -1                               x  = 2

To check your answers, substitute the solutions back into the original equation and solve.

x^6 - 7x^3 - 8 = 0

-1^6 -7(-1)^3 - 8 = 0          2^6 - 7(2^3) - 8 = 0

1 + 7-8 = 0                            64 - 7(8) - 8 = 0

8-8 = 0                                  64 - 56 - 8 = 0

0 = 0 checks                             0=0 checks