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

Condition:

Solve each quadratic in form equation.

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

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

Solution:

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

Let $u = x - 5$

$u^2 + 2u - 35 = 0 \rightarrow (u + 7)(u - 5) = 0 \rightarrow (x - 5 + 7)(x - 5 - 5) = 0$

$(x + 2)(x - 10) = 0$

4: $(x - 2)^2 - 3(x - 2) + 2 = 0$

$u^2 - 3u + 2 = 0$ Where $u = x - 2$

$(u - 1)(u - 2) = 0 \rightarrow (x - 2 - 1)(x - 2 - 2) = 0$

$(x - 3)(x - 4) = 0$

Answer: 3: $x_1 = -2, x_2 = 10$;

4: $x_1 = 3, x_2 = 4$.