how do you solve quadratic equations by factoring?
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To solve quadratic equations by factoring, follow these steps:
Step 1: Express the equation in quadratic form
Make sure the equation is in the form of ax^2 + bx + c = 0, where a, b, and c are constant coefficients.
Step 2: Factor the equation
Look for two numbers that multiply to give the constant term (c) and add up to give the coefficient of the middle term (b).
Step 3: Set each factor equal to zero
Once you have factored the equation, set each factor equal to zero. This will give you multiple equations to solve.
Step 4: Solve for the variable
Solve each equation from step 3 by isolating the variable on one side.
Step 5: Check for extraneous solutions
After solving for the variable, plug the solutions back into the original equation and check if they satisfy the equation. Eliminate any solutions that make the equation false.
By following these steps, you can solve quadratic equations by factoring.