Questions on Word Problems: Evaluation, Substitution answered by real tutors!

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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
: 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(9368) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given equations.

g(x)=2x^2 -8 and k(x) =-x^2 -2


Since g(x)=k(x), this means that 2x^2 -8=-x^2 -2




2x^2-8=-x^2-2 Start with the given equation.


2x^2-8+1x^2+2=0 Add x^2 to both sides. Add 2 to both sides.


3x^2-6=0 Combine like terms.


Notice we have a quadratic equation in the form of ax^2+bx+c where a=3, b=0, and c=-6


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(0) +- sqrt( (0)^2-4(3)(-6) ))/(2(3)) Plug in a=3, b=0, and c=-6


x = (-0 +- sqrt( 0-4(3)(-6) ))/(2(3)) Square 0 to get 0.


x = (-0 +- sqrt( 0--72 ))/(2(3)) Multiply 4(3)(-6) to get -72


x = (-0 +- sqrt( 0+72 ))/(2(3)) Rewrite sqrt(0--72) as sqrt(0+72)


x = (-0 +- sqrt( 72 ))/(2(3)) Add 0 to 72 to get 72


x = (-0 +- sqrt( 72 ))/(6) Multiply 2 and 3 to get 6.


x = (-0 +- 6*sqrt(2))/(6) Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x = (-0)/(6) +- (6*sqrt(2))/(6) Break up the fraction.


x = 0 +- sqrt(2) Reduce.


x = sqrt(2) or x = -sqrt(2) Break up the expression.


So the answers are x = sqrt(2) or x = -sqrt(2)


which approximate to x=1.414 or x=-1.414