Question

what are the solutions of the quadratic equation ((x + 3)^2 = 49)?
(x = 2) and (x = sqrt{-10})
(x = 4) and (x = -10)
(x = 40) and (x = -58)
(x = -2) and (x = -16)

Explanation:

Step1: Take square roots of both sides

$$\sqrt{(x+3)^2} = \pm\sqrt{49}$$
$$x+3 = \pm7$$

Step2: Solve for positive root

$$x+3 = 7$$
$$x = 7 - 3 = 4$$

Step3: Solve for negative root

$$x+3 = -7$$
$$x = -7 - 3 = -10$$

Answer:

$x = 4$ and $x = -10$