President Barack Obama said Tuesday that he intends to “finish the job” in Afghanistan and has decided on how many new troops to send.

Obama’s announcement, expected in a presidential television address next Tuesday, comes after weeks of study that some critics have denounced as dithering. A three-month review has been punctuated by differences in his administration and concerns about corruption in Kabul.

Obama must decide whether to add as many as 40,000 troops to an 8-year-old war that began after the Sept. 11 attacks and has begun to try the patience of Americans as the Taliban insurgency has gained strength.