How do you solve 6x ^ { 2} - 5= 4?

3 Answers
Oct 2, 2017

x=sqrt(3/2) or x=-sqrt(3/2)

Explanation:

First we subtract 4 from both sides.
6x^2-5=4
6x^2-5color(blue)-color(blue)4=4color(blue)-color(blue)4
6x^2-9=0

Next we add 5 to both sides of the equation:
6x^2-5color(blue)+color(blue)5=4color(blue)+color(blue)5->
6x^2=9

Divide both sides by 6:
(6x^2)/6=9/6->

x^2=9/6->

x^2=3/2

We will solve x^2=3/2 using this:If x^2=y, then x=sqrty or -sqrty

Therefore, x=sqrt(3/2) or x=-sqrt(3/2)

Just for fun: x=1.2247... x=1.2247...

Oct 2, 2017

Solution : x =sqrt (3/2) , x = - sqrt (3/2)

Explanation:

6x^2-5=4 or 6x^2=5+4 or 6x^2=9 or

x^2=9/6 or x^2 = 3/2 or x = +- sqrt (3/2)

Solution : x =sqrt (3/2) , x = - sqrt (3/2) [Ans]

Oct 2, 2017

x=+-sqrt(3/2)

Explanation:

"isolate the "x^2" term by manipulations"

"add 5 to both sides"

6x^2cancel(-5)cancel(+5)=4+5

rArr6x^2=9

"divide both sides by 6"

(cancel(6)x^2 )/cancel(6)=9/6=3/2

rArrx^2=3/2

color(blue)"take the square root of both sides"

sqrt(x^2)=+-sqrt(3/2)larr" note plus or minus"

rArrx=+-sqrt(3/2)larr" exact solutions"