Right angles triangle
|\
| \
x| \ 50
| \
| \
_____
x+10
Using Pythagoras Theorem
(Opposite^2)+(adjacent^2)=(hypotenuse^2)
:- (x+10)^2 + (x)^2 = 50^2
= (x^2)+20x+100+(x^2)=50^2
Collect like terms
(x^2)+(x^2)+20x+100=2500
2(x^2)+20x+100-2500=0
(2x^2)+20x-2400=0
Divide everything by 2 for easy calculation
x^2+10x-1200=0
Using Factorisation by grouping factors
(Factors that when multiplied together gives -1200 but when added gives +10:those factors are 40 and -30)
x^2 + 40x - 30x - 1200=0
(x^2 + 40x) -30x -1200= 0
Factorise
x(x+40) -30(x+40)=0
(x-30)(x+40)=0
For the answer to be 0 one of the factors must be 0 because anything multiplied by 0 is still 0
(x-30) =0 or (x+40)=0
x-30=0 or x+40=0
x=30 or x=-40
:- The values of x are 30 or -40
Take note the use of “OR”and not “AND”