what is the value of x in x^2-4x=3x-2+28

Question

geometry question

Answer 1

x²-4x=3x-2+28=3x+26,

x²-7x-26=0 or x²-7x=26, so complete the square:

x²-7x+49/4=26+49/4=153/4,

(x-7/2)²=153/4,

x-7/2=±√153/2=±√(9×17)/2=±(3/2)√17,

x=7/2±(3/2)√17=9.6847 or -2.6847 approx.

If this is a geometry question and x is the length of a side or line segment, then we must choose the positive value x=9.6847.