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.

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