SOLUTION: xsquared-13x=-10

Algebra ->  Rational-functions -> SOLUTION: xsquared-13x=-10      Log On


   

Question 102474: xsquared-13x=-10
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-13x=-10 Start with the given equation


x%5E2-13x%2B10=0 Add 10 to both sides


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%5E2-13%2Ax%2B10=0 ( notice a=1, b=-13, and c=10)




x+=+%28--13+%2B-+sqrt%28+%28-13%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Plug in a=1, b=-13, and c=10



x+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Negate -13 to get 13



x+=+%2813+%2B-+sqrt%28+169-4%2A1%2A10+%29%29%2F%282%2A1%29 Square -13 to get 169 (note: remember when you square -13, you must square the negative as well. This is because %28-13%29%5E2=-13%2A-13=169.)



x+=+%2813+%2B-+sqrt%28+169%2B-40+%29%29%2F%282%2A1%29 Multiply -4%2A10%2A1 to get -40



x+=+%2813+%2B-+sqrt%28+129+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%2813+%2B-+sqrt%28129%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%2813+%2B-+sqrt%28129%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%2813+%2B+sqrt%28129%29%29%2F2 or x+=+%2813+-+sqrt%28129%29%29%2F2


Now break up the fraction


x=%2B13%2F2%2Bsqrt%28129%29%2F2 or x=%2B13%2F2-sqrt%28129%29%2F2


Simplify


x=13+%2F+2%2Bsqrt%28129%29%2F2 or x=13+%2F+2-sqrt%28129%29%2F2


So these expressions approximate to

x=12.1789083458003 or x=0.821091654199726


So our solutions are:
x=12.1789083458003 or x=0.821091654199726

Notice when we graph x%5E2-13%2Ax%2B10, we get:



when we use the root finder feature on a calculator, we find that x=12.1789083458003 and x=0.821091654199726.So this verifies our answer

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
xsquared-13x=-10
x^2-13x+10=0
Use quadratic formula to get:
x = [13 +- sqrt(169-4*10)]/2
x = [13 +- sqrt(129)]/2
x = 12.179 or x = 0.821
===============
Cheers,
stan H.