How do you solve #\frac { x ^ { 2} } { 15} - 6= - 2#?

1 Answer
smendyka
Dec 8, 2017

See a solution process below:

Explanation:

First, add #color(red)(6)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#x^2/15 - 6 + color(red)(6) = -2 + color(red)(6)#

#x^2/15 - 0 = 4#

#x^2/15 = 4#

Next, multiply each side of the equation by #color(red)(15)# to isolate the #x^2# while keeping the equation balanced:

#color(red)(15) xx x^2/15 = color(red)(15) xx 4#

#cancel(color(red)(15)) xx x^2/color(red)(cancel(color(black)(15))) = 4 xx 15#

#x^2 = 4 xx 15#

Now, take the square root of each side of the equation to solve for #x# while keeping the equation balanced. Remember, the square root of a number produces both a positive and a negative result:

#sqrt(x^2) = +-sqrt(4 xx 15)#

#x = +-sqrt(4)sqrt(15)#

#x = +-2sqrt(15)#

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