Question

What are the real or imaginary solutions of each polynomial equation?
125x+343=0

Answer 1

I bet that is \[125x^3+343=0\]

Answer 2

which is a sum of cubes: \((5x)^3 + (7)^3\)
Factor sum of cubes:
\[a^3+b^3= (a+b)(a^2-ab+b^2)\]

Answer 3

\[(5x+7)((5x)^2-(5x)(7) + (7)^2) = 0\]\[(5x+7)(25x^2-35x+49) = 0\]
\[5x+7=0\]\[x=-\frac{7}{5}\]

\[25x^2-35x+49=0\]Using quadratic formula:\[x = \frac{-(-35)\pm\sqrt{(-35)^2-4(25)(49)}}{2*25}\]\[x = \frac{7}{10}(1\pm i\sqrt{3})\]