How to rearrange the equation?

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In summary, to simplify an equation, you need to combine like terms and use the distributive property. To isolate a variable in an equation, you need to use inverse operations. To solve for multiple variables, you can use substitution or elimination. The steps for rearranging an equation are simplifying, isolating the desired variable, and performing necessary operations. It is possible to change the order of terms in an equation, but caution must be taken to maintain equality.
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I've been trying (unsuccessfully!) to rearrange the following equation so that H is the subject:

mgH = [k(H - L)^2] / 2

(Where ^2 means squared.) I also have some test data which shows that if m = 50, g = 9.8, k = 40 and L = 20, H should equal 57.5, or thereabouts
 
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If you expand the square term, move the left side over to the right, collect terms, you get a quadratic equation in H that you can solve.
 

1. How do I simplify an equation?

To simplify an equation, you need to combine like terms and use the distributive property. This will help you to remove any unnecessary terms and simplify the equation to its most basic form.

2. How do I isolate a variable in an equation?

To isolate a variable in an equation, you need to use inverse operations. This means performing the opposite operation on both sides of the equation until the variable is on one side by itself.

3. How do I solve for multiple variables in an equation?

To solve for multiple variables in an equation, you need to use substitution or elimination. This involves solving for one variable and plugging that value into the other equations to solve for the remaining variables.

4. What are the steps for rearranging an equation?

The steps for rearranging an equation are to first simplify the equation, then isolate the variable you want to rearrange for, and finally perform any necessary operations to get the variable on one side by itself.

5. Can I change the order of terms in an equation?

Yes, you can change the order of terms in an equation as long as you maintain the equality of both sides. However, it is important to be careful when rearranging terms to avoid any errors.

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