SOLUTION: For about what value(s) of x does g(x)=k(x) if g(x)=2x^2 -8 and k(x) =-x^2 -2? x~ +or-2 x~ +or-2.3 x~ 1.4 x~ +or- 1.4

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: For about what value(s) of x does g(x)=k(x) if g(x)=2x^2 -8 and k(x) =-x^2 -2? x~ +or-2 x~ +or-2.3 x~ 1.4 x~ +or- 1.4       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 151501: For about what value(s) of x does g(x)=k(x) if g(x)=2x^2 -8 and k(x) =-x^2 -2?
x~ +or-2
x~ +or-2.3
x~ 1.4
x~ +or- 1.4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given equations.

g%28x%29=2x%5E2+-8 and k%28x%29+=-x%5E2+-2


Since g%28x%29=k%28x%29, this means that 2x%5E2+-8=-x%5E2+-2




2x%5E2-8=-x%5E2-2 Start with the given equation.


2x%5E2-8%2B1x%5E2%2B2=0 Add x%5E2 to both sides. Add 2 to both sides.


3x%5E2-6=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=0, 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-%280%29+%2B-+sqrt%28+%280%29%5E2-4%283%29%28-6%29+%29%29%2F%282%283%29%29 Plug in a=3, b=0, and c=-6


x+=+%28-0+%2B-+sqrt%28+0-4%283%29%28-6%29+%29%29%2F%282%283%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0--72+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-6%29 to get -72


x+=+%28-0+%2B-+sqrt%28+0%2B72+%29%29%2F%282%283%29%29 Rewrite sqrt%280--72%29 as sqrt%280%2B72%29


x+=+%28-0+%2B-+sqrt%28+72+%29%29%2F%282%283%29%29 Add 0 to 72 to get 72


x+=+%28-0+%2B-+sqrt%28+72+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-0+%2B-+6%2Asqrt%282%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-0%29%2F%286%29+%2B-+%286%2Asqrt%282%29%29%2F%286%29 Break up the fraction.


x+=+0+%2B-+sqrt%282%29 Reduce.


x+=+sqrt%282%29 or x+=+-sqrt%282%29 Break up the expression.


So the answers are x+=+sqrt%282%29 or x+=+-sqrt%282%29


which approximate to x=1.414 or x=-1.414