Question

texascollegebridge
study paths initial diagnostic: tx math bridge - stage 2
tx math e
radical expressions and quadratic equations
progress:
the movement of the progress bar may be uneven because questions can be worth more
solve: ((x - 4)^2 + 4 = 49)
(x = -4 + sqrt{45})
(x = -4 pm 2sqrt{10})
(x = pm 7)
(x = 4 pm 3sqrt{5})

Explanation:

Step1: Isolate the squared term

Subtract 4 from both sides:
$(x - 4)^2 = 49 - 4 = 45$

Step2: Take square roots of both sides

$\sqrt{(x - 4)^2} = \pm\sqrt{45}$
$x - 4 = \pm 3\sqrt{5}$ (since $\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}$)

Step3: Solve for x

Add 4 to both sides:
$x = 4 \pm 3\sqrt{5}$

Answer:

D. $x = 4 \pm 3\sqrt{5}$