9514 1404 393
Answer:
{-2.965, -0.464}
Explanation:
A graphing calculator shows the solutions to be about -2.965 and -0.464.
A machine solver for the cubic gives the three solutions as approximately ...
{-2.9650134903182933558,
-0.46362503406015100280,
4.0953051910451110253}
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The attached graph shows the solutions to f(x) = g(x).
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Additional comment
The equation could resolve to a single cubic in standard form:
-3/4x^3 +1/2x^2 +10x -7/9 = |0.5x +2| -7
Multiplying by 36 gives ...
-27x^3 +18x^2 +360x -28 = |18x +72| -252
For the case where x > -4, we can subtract (18x -180) from both sides to get ...
-27x^3 +18x^2 +342x +152 = 0
The roots of this cubic equation are the solutions to f(x) = g(x) as given above. If you want to find them by iteration, a suitable starting point is -152/342 = -4/9.