Question

Solve by using the Square Root Method

3. 3x^2=75

4. (5x+3)^2=12

Answer 1

Solve by using the Square Root Method

3. $3x^2 = 75$

4. $(5x + 3)^2 = 12$

Solution

3.

$$3x^2 = 75,$$ $$x^2 = \frac{75}{3} = 25,$$ $$x = \pm \sqrt{25} = \pm 5.$$

Answer: $x_1 = 5$, $x_2 = -5$.

4.

$$(5x + 3)^2 = 12,$$ $$5x + 3 = \pm \sqrt{12} = \pm 2\sqrt{3};$$

a) $5x + 3 = 2\sqrt{3}, x = \frac{2\sqrt{3} - 3}{5}$;

b) $5x + 3 = -2\sqrt{3}, x = \frac{-2\sqrt{3} - 3}{5}$.

Answer: $x_1 = \frac{2\sqrt{3} - 3}{5}, x_2 = \frac{-2\sqrt{3} - 3}{5}$.