solving equations

-x^2, if x=-1, etc

To solve equations, especially quadratic equations, it's important to understand the basics of substitution. Let's work through the example you've mentioned: solving the equation -x^2 when x is equal to -1.

Step 1: Substitute the value of x into the equation.
-(-1)^2

Step 2: Simplify the expression.
-(1)
-1

So, when x is equal to -1, the value of -x^2 is equal to -1.

Here's a general step-by-step guide to solving quadratic equations:

Step 1: Rewrite the equation in the standard quadratic form:
ax^2 + bx + c = 0

Step 2: Factor the quadratic expression or use the quadratic formula.
If the equation can be factored, factor it into two binomials and set each equal to zero. If not, use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

Step 3: Solve for x by simplifying the equation.
If you factored the equation, you will have two separate equations to solve. If you used the quadratic formula, simplify the expression and calculate the two possible values for x.

Step 4: Verify your solutions.
Plug in the values of x you obtained back into the original equation to confirm if they satisfy it.

Remember to follow these steps whenever you encounter quadratic equations or any other equations you need to solve.