SOLUTION: if the quadratic formula is used to find the roots of the equation x2 - 6x - 19 =0 ((the 2 is the second power)) the correct roots are?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: if the quadratic formula is used to find the roots of the equation x2 - 6x - 19 =0 ((the 2 is the second power)) the correct roots are?      Log On


   

Question 858471: if the quadratic formula is used to find the roots of the equation x2 - 6x - 19 =0 ((the 2 is the second power))
the correct roots are?
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%5E2-6%2Ax-19=0 ( notice a=1, b=-6, and c=-19)





x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A-19+%29%29%2F%282%2A1%29 Plug in a=1, b=-6, and c=-19




x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A-19+%29%29%2F%282%2A1%29 Negate -6 to get 6




x+=+%286+%2B-+sqrt%28+36-4%2A1%2A-19+%29%29%2F%282%2A1%29 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because %28-6%29%5E2=-6%2A-6=36.)




x+=+%286+%2B-+sqrt%28+36%2B76+%29%29%2F%282%2A1%29 Multiply -4%2A-19%2A1 to get 76




x+=+%286+%2B-+sqrt%28+112+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%286+%2B-+4%2Asqrt%287%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+=+%286+%2B-+4%2Asqrt%287%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%286+%2B+4%2Asqrt%287%29%29%2F2 or x+=+%286+-+4%2Asqrt%287%29%29%2F2



Now break up the fraction



x=%2B6%2F2%2B4%2Asqrt%287%29%2F2 or x=%2B6%2F2-4%2Asqrt%287%29%2F2



Simplify



x=3%2B2%2Asqrt%287%29 or x=3-2%2Asqrt%287%29



So the solutions are:

x=3%2B2%2Asqrt%287%29 or x=3-2%2Asqrt%287%29