SOLUTION: the problem is: -3x(squared)+6x+23=0 I understand how to do the formula, but when I try to get my answers for x, they are different then the answer on the answer sheet. Can you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: the problem is: -3x(squared)+6x+23=0 I understand how to do the formula, but when I try to get my answers for x, they are different then the answer on the answer sheet. Can you      Log On


   

Question 94356: the problem is:
-3x(squared)+6x+23=0
I understand how to do the formula, but when I try to get my answers for x, they are different then the answer on the answer sheet. Can you break down the problem for me please?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 -3%2Ax%5E2%2B6%2Ax%2B23=0 ( notice a=-3, b=6, and c=23)

x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A-3%2A23+%29%29%2F%282%2A-3%29 Plug in a=-3, b=6, and c=23



x+=+%28-6+%2B-+sqrt%28+36-4%2A-3%2A23+%29%29%2F%282%2A-3%29 Square 6 to get 36



x+=+%28-6+%2B-+sqrt%28+36%2B276+%29%29%2F%282%2A-3%29 Multiply -4%2A23%2A-3 to get 276



x+=+%28-6+%2B-+sqrt%28+312+%29%29%2F%282%2A-3%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+2%2Asqrt%2878%29%29%2F%282%2A-3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-6+%2B-+2%2Asqrt%2878%29%29%2F-6 Multiply 2 and -3 to get -6

So now the expression breaks down into two parts

x+=+%28-6+%2B+2%2Asqrt%2878%29%29%2F-6 or x+=+%28-6+-+2%2Asqrt%2878%29%29%2F-6


Now break up the fraction


x=-6%2F-6%2B2%2Asqrt%2878%29%2F-6 or x=-6%2F-6-2%2Asqrt%2878%29%2F-6


Simplify


x=1-sqrt%2878%29%2F3 or x=1%2Bsqrt%2878%29%2F3


So these expressions approximate to

x=-1.94392028877595 or x=3.94392028877595


So our solutions are:
x=-1.94392028877595 or x=3.94392028877595

Notice when we graph -3%2Ax%5E2%2B6%2Ax%2B23, we get:



when we use the root finder feature on a calculator, we find that x=-1.94392028877595 and x=3.94392028877595.So this verifies our answer