SOLUTION: How do yu solve this by using quadratic formula 3x (3x + 4) = -4 ? please show steps.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How do yu solve this by using quadratic formula 3x (3x + 4) = -4 ? please show steps.      Log On


   

Question 149479: How do yu solve this by using quadratic formula 3x (3x + 4) = -4 ?
please show steps.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x+%283x+%2B+4%29+=+-4 Start with the given equation.


9x%5E2+%2B+12x=+-4 Distribute.

9x%5E2%2B12x%2B4=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=9, b=12, and c=4


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-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%289%29%284%29+%29%29%2F%282%289%29%29 Plug in a=9, b=12, and c=4


x+=+%28-12+%2B-+sqrt%28+144-4%289%29%284%29+%29%29%2F%282%289%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-144+%29%29%2F%282%289%29%29 Multiply 4%289%29%284%29 to get 144


x+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%282%289%29%29 Subtract 144 from 144 to get 0


x+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28-12+%2B-+0%29%2F%2818%29 Take the square root of 0 to get 0.


x+=+%28-12+%2B+0%29%2F%2818%29 or x+=+%28-12+-+0%29%2F%2818%29 Break up the expression.


x+=+%28-12%29%2F%2818%29 or x+=++%28-12%29%2F%2818%29 Combine like terms.


x+=+-2%2F3 or x+=+-2%2F3 Simplify.


So the answer is x+=+-2%2F3 (with a multiplicity of 2).