-2x^4+9=3x+5 Round two decimals

-2x^4+9=3x+5

-9 -9
-2x^4=3x-4
/-2 /-2
x^4=-1.5x+2
that's the most simplified I can get this.

Thank you!

To solve the equation -2x^4 + 9 = 3x + 5 and round to two decimal places, we need to follow these steps:

1. Move all terms to one side of the equation to set it equal to zero:
-2x^4 + 9 - (3x + 5) = 0

2. Combine like terms:
-2x^4 + 9 - 3x - 5 = 0
-2x^4 - 3x + 4 = 0

3. Since this is a fourth-degree equation, it may not have a simple algebraic solution. We can use numerical methods to approximate the solutions. One such method is the Newton-Raphson method:

a. Start by guessing a value for x. Let's say x = 0.
b. Plug this value into the equation to find the corresponding y-value:
-2(0)^4 - 3(0) + 4 = 4

c. Calculate the derivative of the equation with respect to x:
f'(x) = -8x^3 - 3

d. Use the following formula to iteratively update the guess for x until we get closer to the solution:
x_new = x - (f(x) / f'(x))

Here, f(x) = -2x^4 - 3x + 4, and we use the initial guess of x = 0:
x_new = 0 - (4 / (-8(0)^3 - 3))
x_new = 0 - (4 / -3)
x_new ≈ 1.33

e. Repeat steps b-d, using x_new as the new guess, until we achieve the desired level of accuracy (in this case, rounding to two decimal places).

Using this iterative method, we can find the approximate solutions to the equation.