Solve quadratic equation by completing the square. Express answer as exact roots ?
1 Answer
Mar 7, 2018
Explanation:
The steps I will use are:
-
Premultiply by
12 to make the leading term a perfect square and all of the coefficients of the quadratic into integers. -
Complete the square by expressing in the form
(ax)^2+2(ax)(b)+(b)^2-c . -
Use the difference of squares identity to factor
A^2-B^2 = (A-B)(A+B) . -
Simplify and deduce roots.
So:
0 = 12(3/4x^2+6x+1)
color(white)(0) = 9x^2+72x+12
color(white)(0) = (3x)^2+2(3x)(12)+(12)^2-132
color(white)(0) = (3x+12)^2-(2sqrt(33))^2
color(white)(0) = ((3x+12)-2sqrt(33))((3x+12)+2sqrt(33))
color(white)(0) = (3x+12-2sqrt(33))(3x+12+2sqrt(33))
Hence:
3x = -12+-sqrt(33)
So:
x = 1/3(-12+-2sqrt(33)) = -4+-2/3sqrt(33)