Factorise and solve: x^2 - 8x = -15
Step 1: The first step is to rewrite the equation in the form ax2 + bx + c = 0. So in this case, we achieve this by adding 15 to both sides: x2 - 8x + 15 = -15 + 15
x2 - 8x + 15 = 0
Step 2: Now we need to factorise the equation. To factorise this equation we start with finding two numbers which add up to -8 and multiply to make 15. These numbers must be -5 and -3. So the factorisation of this equation is: (x - 5)(x - 3) = 0
Step 3: Finally, we can solve by saying:
x - 5 = 0 or x - 3 = 0, so
x = 5 or x = 3
CHECK: You can check your two answers, 5 and 3, by subsituting them into the orginal equation, x2 - 8x = -15.
So firstly for x = 5: (5)2 - 8(5) = -15
25 - 40 = -15
-15 = -15 which is clearly true, so we have confirmed that x = 5 is a solution.
We can proceed in exactly the same way for x = 3, and if you try it you will find that it works out and we can confirm that x = 3 is a solution too.
NEAT ANSWER: Here is an example what you should write in the exam to get full marks:
x2 - 8x = -15
x2 - 8x + 15 = 0
(x - 5)(x - 3) = 0
So, x = 5 or x = 3
