What is the answer to 2sqrt(x)= 2/3 x^2-16/3 x ?

The answer to 2sqrt(x)= 2/3 x^2-16/3 x is x=0,x=9

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2sqrt(x)= 2/3 x^2-16/3 x

2 x = \frac{2}{3} x^{2} - \frac{16}{3} x

x = 0, x = 9

Solution steps

2 x = \frac{2}{3} x^{2} - \frac{16}{3} x

Multiply both sides by

3

2 x \cdot 3 = \frac{2}{3} x^{2} \cdot 3 - \frac{16}{3} x \cdot 3

Simplify

6 x = 2 x^{2} - 16 x

Square both sides:

36 x = 4 x^{4} - 64 x^{3} + 256 x^{2}

36 x = 4 x^{4} - 64 x^{3} + 256 x^{2}

Solve

36 x = 4 x^{4} - 64 x^{3} + 256 x^{2} : x = 0, x = 9, x = \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}

x = 0, x = 9, x = \frac{7 + 3 5}{2}, x = \frac{7 - 3 5}{2}

Verify Solutions:

x = 0

True

, x = 9

True

, x = \frac{7 + 3 5}{2}

False

, x = \frac{7 - 3 5}{2}

False

The solutions are

x = 0, x = 9

(x - 4)^{2} = - 1

x + 2 - x = 1

x, 16 x - 40 x^{\frac{1}{2}} + 9 = 0

a, (2 - j 3) = a + jb

x = 8 x - 9

What is the answer to 2sqrt(x)= 2/3 x^2-16/3 x ?
The answer to 2sqrt(x)= 2/3 x^2-16/3 x is x=0,x=9
Solve for x: 2sqrt(x)= 2/3 x^2-16/3 x
The solution is x=0,x=9