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D2. Elementary algebra : solving quadratic equations. Any equation formed using a quadratic function is called a quadratic equation. All these equations are quadratic equations: x2 + 7x - 11=0, x2 - 12x =4, x2 + 14=x, 6x2 + x - 1=0, 5 - x2=0 Generally, quadratic equations have the form: ax2 + bx + c=0, where a, b and c are numbers and a ¹ 0 A quadratic equation like x2 + 3x + 2=0 can be solved by factorising. Because x2 + 3x + 2=(x + 1)(x + 2) we can write the quadratic equation as: (x + 1)(x + 2)=0 Now we know that either x + 1=0 or x + 2=0. So the two solutions to the equation are -1 and -2. Example: solve x2 + 4x + 3=0 Step 1: Factorise (x + 3)(x + 1)=0 Step 2: Write down the two solutions: -3 and -1 Step 3 Check your answers fit the original equation   Example: Solve x2 - 2x - 3=0 Step 1: Factorise (x + 1)(x - 3)=0 Step 2: Write down the two solutions: -1 and 3 Step 3: Check your answers fit the original equation   Here's another way of showing the process. Change the values of the variables a and b. Not all quadratic functions can be easily factorised though. If the following display becomes complicated for a particular value of a and b, you will have to wait until your AS/A2 course covers this topic for a detailed explanation. Practise solving quadratic equations. Press "Solve" to get started. 2 + x + =0 x=  or x=