HOW WOULD I SOLVE SOMETHING LIKE THIS, IT IS AN EXAMPLE I MADE UP. ITS SIMILAR TO THE ONE I HAVE. I DON'T GET IT. THERE ARE TWO UNKNOW VARILABLES AND SOME NUMBERS. HOW DO I POSSIBLE SOLVE THIS. MAYBE I DON'T HAVE TO SOLVE ANYTHING THAT IS WHAT I WAS THINKING.
QUESTION:
2x^2-10x/x^2-5x= x-3
There is only one unknown x.
To solve the equation 2x^2 - 10x / (x^2 - 5x) = x - 3, you need to isolate the variable x on one side of the equation. Here's a step-by-step process to solve it:
1. Simplify both sides of the equation by multiplying both sides by the denominator (x^2 - 5x) to eliminate the fraction:
(2x^2 - 10x) * (x^2 - 5x) / (x^2 - 5x) = (x - 3) * (x^2 - 5x) / (x^2 - 5x)
Simplifying further:
2x^2 - 10x = (x^3 - 8x^2 - 5x^2 + 15x) / (x^2 - 5x)
2. Expand the numerator on the right side:
2x^2 - 10x = (x^3 - 13x^2 + 15x) / (x^2 - 5x)
3. Multiply both sides of the equation by (x^2 - 5x) to eliminate the fraction:
(2x^2 - 10x) * (x^2 - 5x) = (x^3 - 13x^2 + 15x) * (x^2 - 5x)
4. Expand both sides by distributing:
(2x^4 - 20x^3 - 10x^3 + 100x^2) = (x^5 - 18x^4 + 80x^2 - 75x^3)
5. Simplify and rewrite the equation:
2x^4 - 30x^3 + 100x^2 = x^5 - 18x^4 - 75x^3 + 80x^2
Now, this equation is a fifth-degree polynomial equation. Solving polynomial equations of degree five or higher is generally complex and requires advanced techniques. If you do not have a specific method or technique to solve such equations, you may need to use graphing software or numerical methods to estimate the roots.
However, if this equation is not critical and you're just looking for a rough approximation or to explore the behavior of the equation, a graphing calculator or software can help you visualize the equation and identify any possible solutions.