SOLUTION: Demonstrate how your quadratic equation is solved by the Quadratic Formula. Explain your steps. 7. <a href="http://www.codecogs.com/eqnedit.php?latex=x^2 @plus; 13= 4x" target="_b

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Demonstrate how your quadratic equation is solved by the Quadratic Formula. Explain your steps. 7. <a href="http://www.codecogs.com/eqnedit.php?latex=x^2 @plus; 13= 4x" target="_b      Log On


   

Question 397233: Demonstrate how your quadratic equation is solved by the Quadratic Formula. Explain your steps.
7.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Enter the coefficients of the quadratic in the form of ax%5E2+%2B+bx+%2B+c=0

x%5E2+%2B+13=+4x
x%5E2+-4x+%2B+13=+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%5E2-4%2Ax%2B13=0 ( notice a=1, b=-4, and c=13)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=13




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A1%2A13+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)




x+=+%284+%2B-+sqrt%28+16%2B-52+%29%29%2F%282%2A1%29 Multiply -4%2A13%2A1 to get -52




x+=+%284+%2B-+sqrt%28+-36+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+6%2Ai%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%284+%2B-+6%2Ai%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=2%2B3%2Ai or x=2-3%2Ai