Question

Solve each quadratic in form equation.

3. (x-5)^2+2(x-5)-35=0

4. (x-2)^2-3(x-2)+2=0

Answer 1

Question 22675

3. $(x - 5)^{2} + 2(x - 5) - 35 = 0$

Let $t = x - 5$ , so $t^2 + 2t - 35 = 0$ . $D = 4 - 4 \cdot (-35) = 144$ . $t_{1,2} = \frac{-2 \pm \sqrt{144}}{2} = 5; -7$

, and $x_{1,2} = 10; -2$

4. $(x - 2)^{2} - 3(x - 2) + 2 = 0$ , $t = x - 2$

$t^2 - 3t + 2 = 0$ , $D = 9 - 4 \cdot 2 = 1, t_{1,2} = \frac{3 \pm 1}{2} = 2; 1$ , so $x_{1,2} = 4; 3$