What is the step by step method for solving S=ur+1/2r²
To solve the equation S = ur + 1/2r², where S, u, and r are variables, you can follow these steps:
1. Identify what you are solving for: It is not clear from the equation what you are solving for. Let's assume you want to solve for r.
2. Rearrange the equation: In order to solve for r, we need to rearrange the equation to isolate r on one side. The given equation is S = ur + 1/2r². Subtracting ur from both sides, we get 1/2r² = S - ur.
3. Multiply by 2: Multiply each term in the equation by 2 to eliminate the fraction: 2 * (1/2r²) = 2 * (S - ur), which simplifies to r² = 2(S - ur).
4. Divide by 2: Divide both sides of the equation by 2 to isolate r²: r²/2 = (2(S - ur))/2, resulting in r²/2 = S - ur.
5. Add ur to both sides: Add ur to both sides of the equation to isolate S: r²/2 + ur = S - ur + ur, which simplifies to r²/2 + ur = S.
6. Multiply by 2: Multiply each term in the equation by 2 to eliminate the fraction: 2 * (r²/2 + ur) = 2 * S, which simplifies to r² + 2ur = 2S.
7. Rearrange the equation: The equation is now r² + 2ur = 2S. We can rearrange it to the standard quadratic form, which is easier to solve: r² + 2ur - 2S = 0.
8. Solve the quadratic equation: The equation r² + 2ur - 2S = 0 is a quadratic equation in terms of r. You can solve it using various methods, such as factoring, completing the square, or using the quadratic formula. Once you determine the root(s) of the quadratic equation, you will find the solution(s) for r.
Note that if you are solving for a different variable, such as determining u or S, you would follow a similar process but rearrange the equation accordingly.