What is the solution set for if
What is the solution set for
First, we square both sides to get rid of the radical.
(x – 2)2 = 10x + 19
x2 – 4x + 4 = 10x + 19
x2 – 14x – 15 = 0
(x – 15)(x + 1) = 0
x = 15 OR x = –1
We've done the algebra correctly and got two solutions, but we can't assume that both work. We have to check each one in the original equation.
Check x = 15:
left side = 15 – 2 = 13
right side = = 13
The two sides are equal, so x = 15 is valid solution.
Check x = –1:
left side = (–1) – 2 = –3
right side = = +3
Since the radical symbol ( √ ) means to take the positive root only, the two sides have opposite signs and so are not equal. This means that x = –1 is not a solution.
The only solution is x = 15.
Answer = (C)
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