Solve the quadratic equation x^2 + 7x + 6 = 0
To solve a quadratic equation of the form Ax2 + Bx + C = 0, where, in this example, A=1, B=7 and C=6, we need to factorise the left-hand side of the equation. To do this we first need to write the factors of the number corresponding to C. In this question C = 6 and the factors of 6 are 1,6 and 2,3. The only pair that add up to 7 (the number corresponding to the letter B) is 1 and 6. To write the factorised quadratic we write out two brackets as follows (x + 1)(x + 6).
Using the factorised equation as the left-hand side we have (x+1)(x+6) = 0. To solve this, we need to consider how we get an answer of zero through multiplication. The only way to get an answer of zero is to multiply by zero. Using this information we know that one of the two brackets must, therefore, be equal to zero. As this is a quadratic we have two possible answers. So we have either (x+1) = 0 or (x+6) = 0 and from that we have either x = -1 or x = -6.
