Solve the equation: x^2 + 9x + 20 = 0
This is a quadratic equation. There are different ways to solve quadratic equations including factorising them and using the quadratic formula. This is a simple equation so it cn be solved by factorising. It is not always possible to tell at first glance whether you will be able to factorise a quadratic equation, you may have to attmept it to find out. However, often the way the question is written will let you know. They may say "Solve this equation by factorising it" or "Solve this equation using the quaratic formula." What is factorising? Factorising means finding factors. Factors are expressions that when multiplied together produce the original expression. For example, 1 and 5 are factors of the number 5. In this example, x2 + 9x + 20 = 0. We are aiming to make the expression look like this (ax + b)(cx + d) = 0. The two x values (a and c) need to multipy to produce the number in front of the x2 , in this case it is 1 so a and c will both be 1. The two number values (b and d) must multiply to produce the number in the original expression, in this case 20. So b and d could be 4 and 5 or 10 and 2 or 20 and 1. Finally, these two numbers need to add togther to produce the middle part of the expression, in this case -9x. From our options, we can see that 4 and 5 are the only pair that add up to 9. Therefore, we can write the expression at (x + 4)(x + 5) = 0. From this we can see that either (x + 4) = 0 or (x + 5) = 0. We can solve these smaller equations to show that x = - 4 or x = - 5.
