Question

1. solve the equation below. give your answer(s) in simplest form.

$17 = 11 + 2sqrt4{16 - 5p}$
(handwritten steps: $2sqrt4{16 - 5p}=17 - 11 = 6$; $sqrt4{16 - 5p}=3$; $16 - 5p = 81$; $-5p = 81 - 16 = 65$; $p = -13$)
$p = $

Explanation:

Step1: Isolate the radical term

Subtract 11 from both sides:
$17 - 11 = 2\sqrt[4]{16-5p}$
$6 = 2\sqrt[4]{16-5p}$

Step2: Simplify the radical coefficient

Divide both sides by 2:
$\frac{6}{2} = \sqrt[4]{16-5p}$
$3 = \sqrt[4]{16-5p}$

Step3: Eliminate the 4th root

Raise both sides to the 4th power:
$3^4 = (\sqrt[4]{16-5p})^4$
$81 = 16 - 5p$

Step4: Isolate the variable term

Subtract 16 from both sides:
$81 - 16 = -5p$
$65 = -5p$

Step5: Solve for $p$

Divide both sides by -5:
$p = \frac{65}{-5}$

Answer:

$p = -13$