SOLUTION: Can someone please help with the following? Use the quadratic formula to solve the equation. 2x^2-3x=-6 (Type an exact answer, using radicals as needed. Express complex nu

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone please help with the following? Use the quadratic formula to solve the equation. 2x^2-3x=-6 (Type an exact answer, using radicals as needed. Express complex nu      Log On


   

Question 376647: Can someone please help with the following?
Use the quadratic formula to solve the equation.
2x^2-3x=-6
(Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-3x=-6 Start with the given equation.


2x%5E2-3x%2B6=0 Add 6 to both sides.


Notice that the quadratic 2x%5E2-3x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-3, and C=6


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%282%29%286%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-3, and C=6


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%282%29%286%29+%29%29%2F%282%282%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%282%29%286%29+%29%29%2F%282%282%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-48+%29%29%2F%282%282%29%29 Multiply 4%282%29%286%29 to get 48


x+=+%283+%2B-+sqrt%28+-39+%29%29%2F%282%282%29%29 Subtract 48 from 9 to get -39


x+=+%283+%2B-+sqrt%28+-39+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%283%2Bi%2Asqrt%2839%29%29%2F%284%29 or x+=+%283-i%2Asqrt%2839%29%29%2F%284%29 Break up the expression.


So the solutions are x+=+%283%2Bi%2Asqrt%2839%29%29%2F%284%29 or x+=+%283-i%2Asqrt%2839%29%29%2F%284%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim