SOLUTION: What is the only solution for x in the equation x² -16x + 64 = 0?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: What is the only solution for x in the equation x² -16x + 64 = 0?      Log On


   

Question 288680: What is the only solution for x in the equation
x² -16x + 64 = 0?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-16%2Ax%2B64=0 ( notice a=1, b=-16, and c=64)





x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A64+%29%29%2F%282%2A1%29 Plug in a=1, b=-16, and c=64




x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A1%2A64+%29%29%2F%282%2A1%29 Negate -16 to get 16




x+=+%2816+%2B-+sqrt%28+256-4%2A1%2A64+%29%29%2F%282%2A1%29 Square -16 to get 256 (note: remember when you square -16, you must square the negative as well. This is because %28-16%29%5E2=-16%2A-16=256.)




x+=+%2816+%2B-+sqrt%28+256%2B-256+%29%29%2F%282%2A1%29 Multiply -4%2A64%2A1 to get -256




x+=+%2816+%2B-+sqrt%28+0+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2816+%2B-+0%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2816+%2B-+0%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2816+%2B+0%29%2F2 or x+=+%2816+-+0%29%2F2


Lets look at the first part:


x=%2816+%2B+0%29%2F2


x=16%2F2 Add the terms in the numerator

x=8 Divide


So one answer is

x=8




Now lets look at the second part:


x=%2816+-+0%29%2F2


x=16%2F2 Subtract the terms in the numerator

x=8 Divide


So another answer is

x=8


So our solutions are:

x=8 or x=8


which means we only have one solution


x=8