Quadratic Equations Common Mistakes Quadratic Equations – Square Root Property How to use the Square Root Property Isolate the Squared variable(s). 2( x + 2) 2 = 4 ( x + 2) 2 = 2 Take the square root of both sides of the equation and solve. Common Mistakes Taking the square root before isolating the variable. Taking the square root incorrectly, for example, the 2 below. The square root of 2 is NOT 2. Forgetting to put the plus and minus signs before the square root sign. Incorrect: Add a plus/minus sign in front of the square root. 2x2 = 6 2x = 3 3 x= 2 ( x + 2) 2 = ± 2 x+2=± 2 x = −2 ± 2 2x2 = 6 Correct: 2x2 = 6 x2 = 3 x2 = 3 x=± 3 Complete Manual: Quadratic Equation Review.docx To view right click to open the hyperlink Quadratic Equations – Completing the Square How to Complete the Square If there is a number in front of the x squared, divide it from every term in the equation. Common Mistakes Forgetting to divide the coefficient of x squared from the equation. This will make everything following incorrect. Not understanding how to write the trinomial as a binomial squared. 2 x 2 + 8 x − 10 = 0 x2 + 4x − 5 = 0 Move the numbers to the right and the variables to the left. x2 + 4x = 5 Take the x coefficient, divide it by two and square it. Add this to both sides of the equation. 2 4 2 = (2 ) = 4 2 2 x + 4x + 4 = 5 + 4 x2 + 4x + 4 = 5 + 4 Use the Square Root Property and solve. (x + 2)2 =± 9 x + 2 = ±3 x = −2 ± 3 x = −5,1 Complete Manual: Quadratic Equation Review.docx To view right click to open the hyperlink. Take the square root of the first term – this is the first term of the binomial. Take the square root of the last term – this is the last term of the binomial. Take the middle sign. x2 + 4x + 4 ( x + 2) 2 Re-write the trinomial as a perfect square binomial. ( x + 2) 2 = 9 Not understanding how to use the square root property. Quadratic Equations – Quadratic Formula How to use the Quadratic Formula Formula: − b ± b 2 − 4ac x= 2a Common Mistakes Not knowing the formula Canceling incorrectly. Equation: ax 2 + bx + c Discriminant If the discriminant is >0; there are two real solutions If the discriminant is < than 0; there are two imaginary solutions. If the discriminant is = to 0; there is one real solution. Complete Manual: Quadratic Equation Review.docx To view right click to open the hyperlink. The 2 can NOT divide into the 6 because it’s inside the radical. x= b 2 − 4ac 2 ± 2 6 1±1 6 = 2 4 In this example, there is a 2 that can be divided from the answer. x= 2±3 6 4 In this example, nothing can be canceled because the number in front of the square root is not divisible by 2. Not knowing how to simplify the radical.