What is the answer to x^{2.5}=20x^{1.25} ?

The answer to x^{2.5}=20x^{1.25} is x=0,x=20^{4/5}

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x^{2.5}=20x^{1.25}

x^{2.5} = 20 x^{1.25}

x = 0, x = 2 0^{\frac{4}{5}}

Decimal Notation

x = 0, x = 10.98560 \dots

Solution steps

x^{2.5} = 20 x^{1.25}

Move

20 x^{1.25}

to the left side

x^{2.5} - 20 x^{1.25} = 0

Factor

x^{2.5} - 20 x^{1.25} : x^{1.25} (x^{1.25} - 20)

x^{1.25} (x^{1.25} - 20) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x^{1.25} = 0 or x^{1.25} - 20 = 0

Solve

x^{1.25} = 0 : x = 0

Solve

x^{1.25} - 20 = 0 : x = 2 0^{\frac{4}{5}}

x = 0, x = 2 0^{\frac{4}{5}}

Verify Solutions:

x = 0

True

, x = 2 0^{\frac{4}{5}}

True

The solutions are

x = 0, x = 2 0^{\frac{4}{5}}

(x - 4) - 5 (x - 4)^{\frac{1}{2}} = 6

5 x + 1 = x + 1

5 x + 1 = x - 4

7 - 2 x = x - 2

x - 3 x - 11 = 5

What is the answer to x^{2.5}=20x^{1.25} ?
The answer to x^{2.5}=20x^{1.25} is x=0,x=20^{4/5}
Solve for x: x^{2.5}=20x^{1.25}
The solution is x=0,x=20^{4/5}