Solve the quadratic equation x^2-6x+5=0
x2 - 6x + 5 = 0.
For simple quadratic equations such as this example we need to factorise the expression into 2 brackets: (x+a)(x+b) = 0.
To find a and b we can expand the brackets to give: x2 + (a+b)x +ab = 0.
Therefore a+b = - 6 and ab=5.
If a+b is negative and ab is positive then a and b must be negative as a negative * another negative = a positive.
We can see in this case that a = -1 and b = -5 (or the other way round).
Therefore: x2 - 6x + 5 = (x-1)(x-5) = 0.
If we take the two brackets separately then: x - 1 = 0 therefore x = 1 and x - 5 = 0 therefore x = 5.
These are the two solutions to the quadratic equation: x = 1, x = 5
