Solve for x: 1x2–10x−45+1x2+10x−29=2x2–10x−69
Let
a=x2−10x−45b=x2+10x−29c=x2−10x−69
1a+1b=2c2ab=c(a+b)2(x2−10x−45)(x2+10x−29)=2(x2−10x−69)(x2−37)
(x2−10x−45)(x2+10x−29)=(x2−10x−69)(x2−37)
Then expand and simplify.
5x3−34x2−265x−624=0
Solving by numerical methods gives x≈12.055.
