(x−2)^2 = 3x+34 What is the smallest solution to the given equation?
Correct answer: 3 (parsed from the explanation — this source omits an answer key for this item)
Explanation
- The correct answer is 3. Squaring both sides of the given equation yields -2 2=3 +34 2-4 +4=3 +34 ^x h x , which can be rewritten as x x x . Subtracting 3x 34 2-7 -30=0 and from both sides of this equation yields x x . This quadratic -10 +3 =0 equation can be rewritten as ^x h^x h . According to the zero product -10 +3 -10=0 +3=0 property, ^x h^x h equals zero when either x or x . Solving =10 =- each of these equations for x yields x or x 3. Therefore, the given 10 - - equation has two solutions, and 3. Of these two solutions, 3 is the smallest solution to the given equation.
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