Question

Brainliest for who can answer first!! (only the first one)
Solve the equation: √x = 3 - (1 / 4)x

Answer 1

Answer:

Let u = √x which gives u2= x and rewrite the given equation in terms of u

u = 3 - u 2 / 4

Multiply all terms by 4, simplify and write the above quadratic in standard form and solve it for u.

u 2 + 4 u - 12 = 0

Two solutions: u = - 6 and u = 2

Use the substitution used above u = √x to solve for x.

u = - 6 = √x has no solution

u = 2 = √x has solution x = 4

Below is shown the graph of the right side of the given equation when written with its right side equal to zero. The x intercept of the graph is the graphical solution to the equation as shown below.

Step-by-step explanation:

Answer 2

Answer: x = 4

Step-by-step explanation:

    Given:

√x = 3 - (1 / 4)x

    Rewrite:

$\displaystyle \sqrt{x} = 3 - \frac{1}{4}x$

    Square both sides:

$\displaystyle (\sqrt{x} )^{2} = (3 - \frac{1}{4} x)^{2}$

$\displaystyle x= \frac{1}{16}x^{2} -\frac{3}{2} +9$

    Set the equation equal to 0:

$\displaystyle \frac{-1}{16}x^{2} +\frac{5}{2} -9=0$

    Use the quadratic formula:

$\displaystyle x=\frac{-b\sqrt{b^{2} -4ac} }{2a}$

$\displaystyle x=\frac{-(\frac{5}{2})\sqrt{(\frac{5}{2})^{2} -4(\frac{-1}{16} )(-9)} }{2(\frac{-1}{16} )}$

x = 4, 36

    Plugging back into equation shows us only one answer works,

x = 4