Factorise and solve 3x^2-x-10=0
Firstly I check that the equation is of the form ax2 +bx+c=0 , here it is in such form as a=3 b=-1 c=-10. Because it is a quadratic equation, it can be factorised into 2 brackets. In each bracket there will be an x component that multiply with each other to make 3x. 3x is prime and has 2 factors, 3 and 1, which become the coefficients for each x component. Next I focus on the b component, which is -1. I want to find 2 factors of -10 that each multiply with either 1 or 3 to make 2 numbers that sum to -1. Here 3(-2) and 1(5) make -6 and 5 which sum to -1. So I insert -2 and 5 into the brackets such that -2 is multiplied by 3x and 5 is multiplied by x giving me (3x+5)(x-2).
Next to solve the equation I make each bracket individually equal to 0, as a product of 2 numbers can only be 0 if at least one of them is 0. Finally I solve each linear equation. 3x+5=0 (subtract 5 from both sides) 3x=-5 (divide both sides by 3) x=-5/3. x-2=0 (add 2 to both sides) x=2. So the solutions are x=-5/3 or x=2.
