We can rewrite the equation as:
(x)^3 + (7)^3 = 0
We can use the sum of cubes formula, which states that: a^3 + b^3 = (a + b)(a^2 - ab + b^2)
So, applying this formula to our equation, we have:
(x + 7)(x^2 - 7x + 7^2) = 0
Now, we can solve for x in each factor:
x + 7 = 0 -> x = -7
x^2 - 7x + 49 = 0
Using the quadratic formula, x = ( -(-7) ± √( (-7)^2 - 4(1)(49) ) ) / (2(1))
Simplifying further, we have x = (7 ± √(-147)) / 2
Since we have a negative value under the square root, the solutions are imaginary.
Thus, the solutions to the equation x^3 + 343 = 0 are -7 and (7 ± √(-147)) / 2.
Find the real or imaginary solutions of the following equation by factoring.
x^3+343=0
1 answer