nchin said:How did this:
kx^(2) = 2mgh + 2mgx
You can do it that way, too. Now multiply every term on both sides by -1i thought it's
kx^(2) = 2mgh + 2mgx
0 = 2mgh + 2mgx - kx^(2) ?
NascentOxygen said:Subtract 2mgh from both sides, then subtract 2mgx from both sides
You can do it that way, too. Now multiply every term on both sides by -1
That gets you the equation that you were expecting to see, but by a different route.nchin said:why do we need to mult both side by -1?
but what if you don't know the correct equation?NascentOxygen said:That gets you the equation that you were expecting to see, but by a different route.
Do you want to solve for x or what?nchin said:How did this:
kx^(2) = 2mgh + 2mgx
become this
kx^(2) - 2mgh - 2mgx = 0
lep11 said:Do you want to solve for x or what?
Okay, now you got kx^(2) - 2mgh - 2mgx = 0 so you can use the quadratic formula to solve for x.nchin said:yes.
It's not wrong. It's perfectly correct.nchin said:but what if you don't know the correct equation?
If i was doing this problem from scratch (without solution manuel)
I wouldn't have known this equation [0 = 2mgh + 2mgx - kx^(2)] was wrong because algebraically, i am correct.
The purpose of manipulating equations in algebra is to solve for a specific variable or to simplify an equation to make it easier to solve. This is a fundamental skill in algebra that helps us understand and solve more complex equations.
To manipulate equations, you can use various algebraic properties and operations such as addition, subtraction, multiplication, and division. You can also use the distributive property, combining like terms, and isolating variables to manipulate equations.
The steps to solving a basic manipulating equation algebra problem are as follows:
Example: Solve for x in the equation 3x + 7 = 22
To solve this equation, we need to isolate the variable x on one side of the equal sign. First, we subtract 7 from both sides to get 3x = 15. Then, we divide both sides by 3 to get x = 5. Therefore, the solution to this equation is x = 5.
To check if your solution is correct, you can substitute the value you found for the variable back into the original equation. If both sides of the equation are equal, then your solution is correct. In our previous example, we can check our solution by substituting x = 5 into the equation 3x + 7 = 22. This gives us 3(5) + 7 = 22, which simplifies to 15 + 7 = 22. Since both sides are equal, we know that our solution of x = 5 is correct.