How to solve 2x-1/3 = x^2+2x/5 using the quadratic formula?
1 Answer
Jan 17, 2016
Explanation:
I am interpreting the given equation as:
#2x-1/3=x^2+(2x)/5#
Move these all to the same side of the equation.
#0=x^2+(2x)/5-2x+1/3#
Simplify the terms with
#0=x^2+(2x)/5-(10x)/5+1/3#
#0=x^2-(8x)/5+1/3#
We could apply the quadratic formula to this, but it would be simpler if we eliminated the fractions. To do this, multiply both sides by
#0=15x^2-24x+5#
We can now use the quadratic formula, which states that for a quadratic function
#x=(-b+-sqrt(b^2-4ac))/(2a)#
Thus,
#x=(-(-24)+-sqrt((-24)^2-(4xx15xx5)))/(2xx15)#
#x=(24+-sqrt(576-300))/30#
#x=(24+-sqrt276)/30#
#x=(24+-sqrt(2^2xx69))/30#
#x=(24+-2sqrt69)/30#
#x=(12+-sqrt69)/15#