Question

solve the quadratic equation using the square root property
$(x + 6)^2 = -49$

the solution set is
(simplify your answer. use a comma to separate answers as needed. type an exact answer, using radicals as needed. express complex numbers in terms of $i$.)

Explanation:

Step1: Apply square root property

Take square roots of both sides:
$$\sqrt{(x+6)^2} = \sqrt{-49}$$
$$x+6 = \pm\sqrt{-49}$$

Step2: Simplify the radical

Rewrite $\sqrt{-49}$ using $i$ (where $i=\sqrt{-1}$):
$$\sqrt{-49} = \sqrt{49 \times (-1)} = \sqrt{49} \times \sqrt{-1} = 7i$$
So:
$$x+6 = \pm7i$$

Step3: Isolate $x$

Subtract 6 from both sides:
$$x = -6 \pm7i$$

Answer:

$\{-6+7i, -6-7i\}$