What does x equal in 5x plus 3x to the power of 2 -2x?

Answer 1

5x + 3x2 - 2x is not an equation, so there is no value of x to be determined. If you want to simplify it, you would get:

5x + 3x2 - 2x

= 3x + 3x2

You could also factor that out, and get 3x(1 + x)

If you want to treat it as a function and find it's range with respect to x, we can see that it describes a parabola. To find it's apex, we can take it's derivative and solve for x = 0:

f(x) = 3x2 + 3x

f'(x) = 6x + 3

0 = 6x + 3

0 = 2x + 1

2x = 1

x = 1/2

Now we can find the corresponding y-coordinate at that x location:

f(1/2) = 3(1/2)2 + 3(1/2)

f(1/2) = 3/4 + 3/2

f(1/2) = 3/4 + 6/4

f(1/2) = 9/4

So the apex of the parabola described by that function occurs at the point (1/2, 9/4). By taking the second derivative (f''(x) = 6), we can see that the rate of change of the slope of the tangent is positive, which means that this is a parabola that moves upwards from it's apex. That tells us that for any real value of x, f(x) will always be greater than or equal to 9/4.