Solving a Quadratic Equation by Using the Quadratic Formula Remember those equations that you were told were un-factorable or prime, and thus could not be solved? Take for example: x 2 10 x 7 0 You cannot solve this equation unless you use either Completing the Square, or the Quadratic Formula (see Math handout # 23 on Completing the Square). One of the desirable qualities of the quadratic formula is that, like all formulas, you just plug numbers into it, and then follow the order of operations until it is solved. You will need to memorize the Quadratic Formula. b b 2 4ac x 2a This is the Quadratic Formula Follow the steps outlined below when using the Quadratic Formula: Step 1: In order to use the quadratic formula, the equation must be in descending order, and set to “0”. Step 2: Label each of the coefficients using “a”, “b”, and “c”. In our example x 2 10 x 7 0 a 1 b 10 c 7 Step 3: Plug the values of a, b, and c into the formula x 10 102 417 21 Step 4: Follow the order of operations to solve for “x”. x 10 100 28 2 x 10 72 2 72 2 x 10 6 2 2 x 5 3 2 and x 5 3 2 The Academic Support Center at Daytona State College (Math 24 pg 1 of 2) 36 If the number under the radical is not a perfect square, try to break it down so that the number under radical can be reduced. Solving a Quadratic Equation by Using the Quadratic Formula (continued) x This is the Quadratic Formula b b 2 4ac 2a Follow the steps outlined below when using the Quadratic Formula: Step 1: In order to use the quadratic formula, the equation must be in descending order, and set to “0”. Step 2: Label each of the coefficients using “a”, “b”, and “c”. In our example 3x 2 5 x 1 0 a 3 b 5 c 1 Step 3: Plug the values of a, b, and c into the formula x 5 52 43 1 23 Step 4: Follow the order of operations to solve for “x”. x 5 25 12 6 x 5 37 6 x 5 37 6 and x The Academic Support Center at Daytona State College (Math 24 pg 2 of 2) 5 37 6

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# Solving a Quadratic Equation