How do you solve #(x - 8)^2 = 48#?

1 Answer
smendyka
Jul 24, 2017

See a solution process below:

Explanation:

First, take the square root of each side of the equation to eliminate the exponent while keeping the equation balanced. Remember, the square root of a number gives both a positive and a negative result:

#sqrt((x - 8)^2) = +-sqrt(48)#

#x - 8 = +sqrt(48)# and #x - 8 = -sqrt(48)#

#x - 8 = sqrt(16 * 3)# and #x - 8 = -sqrt(16 * 3)#

#x - 8 = sqrt(16) * sqrt(3)# and #x - 8 = -sqrt(16)sqrt(3)#

#x - 8 = 4sqrt(3)# and #x - 8 = -4sqrt(3)#

#x - 8 + color(red)(8) = 4sqrt(3) + color(red)(8)# and #x - 8 + color(red)(8) = -4sqrt(3) + color(red)(8)#

#x - 0 = 4sqrt(3) + 8# and #x - 0 = -4sqrt(3) + 8#

#x = 4sqrt(3) + 8# and #x = -4sqrt(3) + 8#

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