Here's a breakdown of the steps:
1. Arrange the equation in standard form:
Make sure the equation is written in the form ax^2 + bx + c = 0, where a, b, and c are coefficients (numbers), and x is the unknown variable.
2. Find two numbers that multiply to ac and add up to b:
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Identify the coefficients a, b, and c from the equation.
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Find two numbers that:
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Multiply together to equal
a x c (the product of the first and last term's coefficients).
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Add up to equal
b (the coefficient of the middle term).
3. Rewrite the middle term using those two numbers:
Replace the middle term (bx) with the sum of the two numbers you just found multiplied by each other.
4. Factor by grouping:
Group the terms so that there's a common factor in each group. Then, factor out the common factors.
5. Simplify the expression:
Combine like terms and write the equation in its factored form.
There are also some special cases where you can use factoring by perfect squares or the sum-product pattern to simplify the process.
If you'd like to see some examples or need help working through a specific quadratic equation, feel free to ask!