solving quadratics:factorisation

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solving quadratics:factorisation

example: X^2 + 7X +10=0 two numbers that add to the middle number but times to the number before the equals symbol.

(X+5)(X+2)=0

x+5=0 x+2=0

x= -5 x=-2 to get this answer you add or subtract the numbers, depending on the symbol inside the bracket

x=-2 or x=-5

harder :

x^2 - x - 6=0

(x-3)(x+2)=0 x=3 or x=-2

6x^2 +13x-5=0

(3x-1)(2x+5)=0

due to there being more than one x we now have to do the calculation: 3x-1=0

, so 3x=1 x=1/3

2x+5 = 0

2x=-5

x=-5/2

factorising without =0

x^2 -4x +18 =4x+2 so we have to simplify this first. we take away the values on the right hand side of the equals from the values on the left hand side.

-4x - 4x = -8x

18 - 2

that now leaves us with: x^2-8x+16=0

from this we can now factorise into: (x-4)(x-4)=0

so x=4