x - 2 2 = 3 x + 34 What is the smallest solution to the given equation?

Question

Accepted Answer

The correct answer is - 3 . Squaring both sides of the given equation yields x - 2 2 = 3 x + 34 , which can be rewritten as x 2 - 4 x + 4 = 3 x + 34 . Subtracting 3 x and 34 from both sides of this equation yields x 2 - 7 x - 30 = 0 . This quadratic equation can be rewritten as x - 10 x + 3 = 0 . According to the zero product property, x - 10 x + 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.

Question x-2-2-