Solve the equation.
-$$\mathrm { s } = 32 + 4 \sqrt { \mathrm { s } }$$
A)128
B)48
C)32
D)64

Question

Quizplus · Accepted Answer

To solve the equation $ s = 32 + 4\sqrt{s} $, let $ x = \sqrt{s} $. Then $ s = x^2 $, and the equation becomes $ x^2 = 32 + 4x $. Rearranging gives $ x^2 - 4x - 32 = 0 $. Solving this quadratic equation using the quadratic formula $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $, where $ a = 1, b = -4, c = -32 $, we find $ x = 8 $ or $ x = -4 $. Since $ x = \sqrt{s} $, $ x $ must be non-negative, so $ x = 8 $. Thus, $ s = x^2 = 8^2 = 64 $.

Solve the Equation s=32+4s\mathrm { s } = 32 + 4 \sqrt { \mathrm { s } }s=32+4s​

Solve the Equation $\mathrm { s } = 32 + 4 \sqrt { \mathrm { s } }$