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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Hard

x - 2 2 = 3 x + 34

What is the smallest solution to the given equation?

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Explanation

The correct answer is -3. Squaring both sides of the given equation yields x-22=3x+34, which can be rewritten as x2-4x+4=3x+34. Subtracting 3 x and 34 from both sides of this equation yields x2-7x-30=0. This quadratic equation can be rewritten as x-10x+3=0. According to the zero product property, x-10x+3 equals zero when either x-10=0 or x+3=0. Solving each of these equations for x yields x=10 or x=-3. Therefore, the given equation has two solutions, 10 and -3 . Of these two solutions, -3 is the smallest solution to the given equation.