SOLUTION: Please show me how to solve this problem, I don't know the steps (btw I'm doing quadratic equations) {{{x^2-10x=-16}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please show me how to solve this problem, I don't know the steps (btw I'm doing quadratic equations) {{{x^2-10x=-16}}}      Log On


   

Question 850573: Please show me how to solve this problem, I don't know the steps (btw I'm doing quadratic equations)
x%5E2-10x=-16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-10x=-16


x%5E2-10x%2B16=0


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%5E2-10%2Ax%2B16=0 ( notice a=1, b=-10, and c=16)





x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29 Plug in a=1, b=-10, and c=16




x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29 Negate -10 to get 10




x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A16+%29%29%2F%282%2A1%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)




x+=+%2810+%2B-+sqrt%28+100%2B-64+%29%29%2F%282%2A1%29 Multiply -4%2A16%2A1 to get -64




x+=+%2810+%2B-+sqrt%28+36+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2810+%2B-+6%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2810+%2B-+6%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2810+%2B+6%29%2F2 or x+=+%2810+-+6%29%2F2


Lets look at the first part:


x=%2810+%2B+6%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=%2810+-+6%29%2F2


x=4%2F2 Subtract the terms in the numerator

x=2 Divide


So another answer is

x=2


So our solutions are:

x=8 or x=2