Solve x^2 + 12 = 6 - 5x by factorisation.
This question is best answered by breaking the process down into a number of smaller steps.Step 1: Rearrange the equation so that both sides are equal to 0 (in other words, add and subtract terms from both sides so that everything is on one side of the equals sign). We will use the fact that both sides equal 0 to help find the solutions after we factorise.Firstly, add 5x to both sides: x2 + 5x + 12 = 6 - 5x + 5xThe -5x and +5x on the right hand side cancel out: x2 + 5x + 12 = 6 - 5x + 5xThen, subtract 6 from both sides: x2 + 5x + 12 - 6 = 6 - 6We can tidy this up like we did before: x2 + 5x + 6 = 6 - 6 + 0Step 2: Now that the equation is in the right form (x2 + 5x + 6 = 0), we can factorise the left hand side.To factorise x2 + 5x + 6, we find two whole numbers that multiply to give 6 and add to give 5.The pairs of numbers that multiply to give 6 are (2,3) and (1,6). Only one of these pairs also add to give 5 - (2,3).We can therefore factorise x2 + 5x + 6 as (x + 2)(x + 3) and write the equation as (x + 2)(x + 3) = 0.Step 3: Use the fact that both sides equal 0 to find solutions for x.Whenever you get 0 by multiplying two numbers, one of the numbers must be 0. In our case, our numbers are (x + 2) and (x + 3).If (x + 2) is 0, then x = -2.If (x + 3) is 0, then x = -3.Therefore the solutions to the equation x2 + 12 = 6 - 5x are:x = -2 or x = -3.
