How do you solve x squared -4x-21 equals 0?

Answer 1

There are 3 main ways to solving a quadratic equation of the from ax2+bx+c=0

The first, also the quickest and easiest, is factorising the equation into the form of (ax+b)(bx+c)=0 implying that either x=-a/b or x=-c/b, for this equation you would factorise into (x-7)(x+3)=0

The second is to use the formula x=(-b±√(b2-4ac))/2a and just put the relative numbers in from your equation.

The final is the 'completing the square' method, where you separate the variable part into the form (x+b/2)2+c-(b/2)2=0 (here we are assuming a=1) leading to x=±√((b/2)2-c)-b/2. This may look more complicated that the formulae method but can sometimes be a lot quicker if you become used to this method and is sometimes needed when the second method leaves you with taking the squareroot of a negative number.

For the equation x2 - 4x - 21=0, it is easiest to use the first or third method, either way you obtain x=7 or -3.