How do you solve by completing the square x^2+3x-8=0?

1 Answer
Apr 3, 2015

Solving a quadratic expression by completing the square means to manipulate the expression in order to write it in the form
(x+a)^2=b
So, if b\ge 0, you can take the square root at both sides to get
x+a=\pm\sqrt{b}
and conclude x=\pm\sqrt{b}-a.

Now, we have (x+a)^2=x^2+2ax+a^2. Since you equation starts with x^2+3x, this means that 2ax=3x, and so a=3/2.
Adding 41/4 at both sides, we have
x^2+3x+9/4=41/4
Which is the form we wanted, because now we have
(x+3/2)^2=41/4
Which leads us to
x+3/2=\pm\sqrt{41/4}=\pm \sqrt{41}/2 and finally x=\pm\sqrt{41}/2-3/2