Mathematics: What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? use u substitution and the quadratic formula to solve. a. x= -8+5 square root 2b) x=-6+5 square root 2c) x= -4+5 square root 2d) x= -2+5 square root 2?

What are the solutions of the equation (x + 2)2

Ответ:

paige3673

13.03.2022

Let u = x+2. That makes our equation, in terms of u: u^2+12u-14=0

. Fitting this into the quadratic formula looks like this: $u= \frac{-12+/- \sqrt{12^2-4(1)(-14)} }{2}$ . Simplifying a bit gives us $u= \frac{-12+/- \sqrt{200} }{2}$ . Simplifying that in terms of the radical gives us $u= \frac{-12+/-10 \sqrt{2} }{2}$ . Reducing that numerator by the 2 in the denominator gives us $u=-6+5 \sqrt{2},-6-5 \sqrt{2}$ . If u = x + 2, then we make that substitution now to solve for x: $x+2=-6+5 \sqrt{2}$ and $x=-10+5 \sqrt{2}$ ; $x+2=-6-5 \sqrt{2}$ and $x=-10-5 \sqrt{2}$