(8x^5+10x^4)-(4x^3-5x)=0
To solve the equation (8x^5 + 10x^4) - (4x^3 - 5x) = 0, you can follow these steps:
Step 1: Simplify the equation
First, distribute the negative sign to the terms inside the parentheses:
8x^5 + 10x^4 - 4x^3 + 5x = 0
Step 2: Rearrange the terms
To make it easier to work with, rearrange the terms in descending order of exponents:
8x^5 + 10x^4 - 4x^3 + 5x = 0
8x^5 + 10x^4 - 4x^3 + 5x + 0 = 0
Step 3: Combine like terms
Combine the terms with the same exponent and add them together:
8x^5 + 10x^4 - 4x^3 + 5x = 0
The equation has no like terms with common exponents, so we cannot simplify it further in this step.
Step 4: Set the equation equal to zero
Move all the terms to one side of the equation by subtracting 0 from both sides:
8x^5 + 10x^4 - 4x^3 + 5x - 0 = 0
8x^5 + 10x^4 - 4x^3 + 5x = 0
Now, the equation is set equal to zero, which is a standard form for polynomial equations.
Step 5: Factor out the common factor (if possible)
There are no common factors that can be factored out from all the terms, so we can't proceed with factoring in this step.
Step 6: Solve for x
To solve for x, you can use various methods such as factoring, the quadratic formula, or graphing. However, the given equation is not simple to solve algebraically. You may need to use numerical methods or graphing to find approximate solutions.
Alternatively, you can use software or online calculators that can solve higher-degree polynomial equations. These tools can provide accurate solutions or approximate solutions to the equation.
So, to find the solutions to the equation (8x^5 + 10x^4) - (4x^3 - 5x) = 0, you can use numerical methods, graphing, or utilize online resources.