Find the real solutions of the equation.
-8x^3-17x^2+7x=0
Factor out the x term, then solve the quadratic in the usual way.
(-x)(8x^2 +17x -7) = 0
(-x)
x = 0 and (1/16)[-17 +/-sqrt513]
x = 0, 0.3531, -2.4781
thank you
To find the real solutions of the equation -8x^3 - 17x^2 + 7x = 0, we can use factoring and the zero product property.
Step 1: Factor out the common factor, x, from the equation:
x(-8x^2 - 17x + 7) = 0
Step 2: Now, we need to solve the equation -8x^2 - 17x + 7 = 0. To do this, we can try factoring or using the quadratic formula.
Step 3: Since the coefficient of x^2 is -8, we need to find two numbers whose product is (8)(7) = 56 and whose sum is -17. After some trial and error, we can see that the numbers are -8 and -7.
Step 4: Rewrite the equation by splitting the middle term using the numbers we found:
-8x^2 - 8x - 9x + 7 = 0
Step 5: Group the terms and factor by grouping:
(-8x^2 - 8x) + (-9x + 7) = 0
-8x(x + 1) - 1(9x - 7) = 0
(-8x - 1)(x + 1) = 0
Step 6: Now we have two linear factors: -8x - 1 = 0 and x + 1 = 0.
For the first factor, -8x - 1 = 0:
-8x = 1
x = -1/8
For the second factor, x + 1 = 0:
x = -1
Step 7: Therefore, the real solutions of the equation -8x^3 - 17x^2 + 7x = 0 are x = -1/8 and x = -1.