find the real solution of the equation by graphing
6x^3-2x=-9x^2
i got 0.2,-1.7 is this correct
6 x ^ 3 - 2 x = - 9 x ^ 2 Add 9 x ^ 2 to both sides
6 x ^ 3 - 2 x + 9 x ^ 2 = - 9 x ^ 2 + 9 x ^ 2
6 x ^ 3 + 9 x ^ 2 - 2 x = 0
x * ( 6 x ^ 2 + 9 x - 2 )= 0
You equation have 3 solutions:
Obviously solution x = 0
Equation :
6 x ^ 2 + 9 x - 2 = 0
have two solutions :
x1/2= [ - 9 + OR - sqrt ( 129 ) ] / 12
3 solutions are :
x1 = 0
x2 = [ - 9 + sqrt ( 129 ) ] / 12
x3 = [ - 9 - sqrt ( 129 ) ] / 12
Your two soutions are correct but polinomial equation of degre 3 have 3 solutions.
Oneof solutions are x = 0
thank you for checking and helping
To find the real solutions of the equation 6x^3 - 2x = -9x^2 by graphing, you will need to follow these steps:
Step 1: Rearrange the equation to bring all terms to one side, so you have: 6x^3 - 9x^2 - 2x = 0.
Step 2: Plot the equation on a graphing tool or software, such as Desmos or GeoGebra.
Step 3: Look for the x-values where the graph intersects the x-axis (i.e., where y = 0). These points represent the real solutions.
From your calculations of 0.2 and -1.7, it seems like you have already performed these steps and found the x-values where the graph crosses the x-axis. If the points are correctly identified, then yes, the solutions 0.2 and -1.7 are correct.
However, I would recommend checking your graph once again to ensure the accuracy of your solutions.