Introduction: Solving an Equation Using the Quadratic Formula
To solve a quadratic equation you can use the quadratic formula in order to find the the two values of x where the equation is solved, or equals 0
Step 1: Gather Supplies
You will need a piece of paper, a writing utensil, and an equation, which will be provided for you.
You may also use a basic calculator in order to perform simple math if necessary.
Step 2: Identify Your Variables
Identify the values of a, b, and c in the given equation. (a) is the coefficient that is in front of the x squared term. (b) is the coefficient that is in front of the x term. (c) is the constant, or the number that is not paired with an x. Write out the a, b, and c values.
If there is no number in front of the x^2 or the x term then the value for a/b is 1. If there is no number at the end then the c value is 0.
Step 3: Write the Formula
Write out the quadratic formula.
Step 4: Plug In
Plug your a, b, and c values into the formula using parentheses to keep all your variables separate.
Insert the “a” value (2) where ever you see an “a.” Insert the “b” value (-8) where ever you see a “b.” Insert the “c” value (-24) where ever you see a “c.” If the variable is negative place the negative sign inside the parentheses.
Step 5: Combine Terms
Begin to simplify the equation by combining the terms underneath the square root.
Step 6: Simplify
Simplify the equation as much as possible by multiplying or taking the square root of the terms.
Step 7: Write 2 Equations
Write two separate equations. The formulas will look exactly the same except one will have a plus sign (+) and one will have a minus sign (-) in place of the (+/-) symbol in the numerator.
Step 8: Add and Subtract
Add the top two terms in the first equation and subtract the top two terms in the second.
Step 9: Simplify
Simplify the fraction by dividing the top by the bottom.
Step 10: Plug in Answers
Plug in the values that you got for x back into the original equation.
Step 11: Check Your Work
Simplify the left side of the equation completely. If you did the problem right, you should end up with 0=0.