SOLUTION: Hi Everyone, I was supposed to solve x^2+10=19....I came up with the solution of +(w/a line under it)3 Am I correct??? I would appreciate anyone reviewing this problem for me...Tha

Algebra ->  Radicals -> SOLUTION: Hi Everyone, I was supposed to solve x^2+10=19....I came up with the solution of +(w/a line under it)3 Am I correct??? I would appreciate anyone reviewing this problem for me...Tha      Log On


   

Question 89352: Hi Everyone, I was supposed to solve x^2+10=19....I came up with the solution of +(w/a line under it)3 Am I correct??? I would appreciate anyone reviewing this problem for me...Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B10=19

x%5E2%2B10-19=0 Subtract 19 from both sides

Now 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%2B10%2Ax-19=0 ( notice a=1, b=10, and c=-19)

x+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A1%2A-19+%29%29%2F%282%2A1%29 Plug in a=1, b=10, and c=-19



x+=+%28-10+%2B-+sqrt%28+100-4%2A1%2A-19+%29%29%2F%282%2A1%29 Square 10 to get 100



x+=+%28-10+%2B-+sqrt%28+100%2B76+%29%29%2F%282%2A1%29 Multiply -4%2A-19%2A1 to get 76



x+=+%28-10+%2B-+sqrt%28+176+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-10+%2B-+4%2Asqrt%2811%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+=+%28-10+%2B-+4%2Asqrt%2811%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-10+%2B+4%2Asqrt%2811%29%29%2F2 or x+=+%28-10+-+4%2Asqrt%2811%29%29%2F2


which split up to


x=-10%2F2%2B4%2Asqrt%2811%29%2F2 or x=-10%2F2-4%2Asqrt%2811%29%2F2


and simplify to


x=-5%2B2%2Asqrt%2811%29 or x=-5-2%2Asqrt%2811%29


Which approximate to

x=1.6332495807108 or x=-11.6332495807108


So our solutions are:
x=1.6332495807108 or x=-11.6332495807108

Notice when we graph x%5E2%2B10%2Ax-19, we get:



when we use the root finder feature on a calculator, we find that x=1.6332495807108 and x=-11.6332495807108.So this verifies our answer