## Answers

One method is factoring. For example, let's try to solve x²+8x=20:

1. First thing that you will do is to transform it into the standard form (ax²+bx+c=0 where a≠0)

x²+8x-20=0

Remember: When moving a term to the other side, the sign will be changed.

2. Factor the quadratic equation:

x²+8x-20=0

(x+10)(x-2)=0

3. Apply the zero product property by setting each factor of the quadratic equation equal to 0.

(x+10)(x-2)=0

x+10=0 x-2=0

Now transpose the variables:

x=-10 x=2

Another method is extracting the square roots.

Example:

x²-4=0

Transpose the variable:

x²-4=0

x²=4

Now, get the square roots:

x²=4

x=2

There are more ways to solve it. But I will just leave the formula:

x=-b plus or minus

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2a

You should already know how to factor quadratics. (If not, review Factoring Quadratics.) The new thing here is that the quadratic is part of an equation, and you're told to solve for the values of x that make the equation true. Here's how it works:

Solve (x – 3)(x – 4) = 0.Okay, this one is already factored for me. But how do I solve this?Think: If I multiply two things together and the result is zero, what can I say about those two things? I can say that at least one of them must also be zero. That is, the only way to multiply and get zero is to multiply by zero. (This is sometimes called "The Zero Factor Property" or "Rule" or "Principle".)Warning: You cannot make this statement about any other number! You can only make the conclusion about the factors ("one of them must equal zero") if the product itself equals zero. If the above product of factors had been equal to, say, 4, then we would still have no idea what was the value of either of the factors; we would not have been able (we would not have been mathematically "justified") in makingany claim about the values of the factors. Because you can only make the conclusion ("one of the factors must have equalled zero") if the product equals zero, you must always have the equation in the form "(quadratic) equals (zero)" before you can attempt to solve it.

The Zero Factor Principle tells me that at least one of the factors must be equal to zero. Since at least one of the factors must be zero, I'll set them eachequal to zero:x – 3 = 0 or x – 4 = 0This gives me simple linear equations, and they're easy to solve:x = 3 or x = 4And this is the solution they're looking for: x = 3, 4Note that "x = 3, 4" means the same thing as "x = 3 or x = 4"; the only difference is the formatting. The "x = 3, 4" format is more-typically used.