What is the answer to 40-0.2x-0.006x^{1.6}=0 ?

The answer to 40-0.2x-0.006x^{1.6}=0 is x=128.75591…,x=-569.95374…

Solve for x: 40-0.2x-0.006x^{1.6}=0

The solution is x=128.75591…,x=-569.95374…

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40 - 0.2 x - 0.006 x^{1.6} = 0

x = 128.75591 \dots, x = - 569.95374 \dots

Solution steps

40 - 0.2 x - 0.006 x^{1.6} = 0

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{1.6} = (x^{\frac{1}{5}})^{(1.6 \cdot 5)}

40 - 0.2 (x^{\frac{1}{5}})^{5} - 0.006 (x^{\frac{1}{5}})^{8} = 0

Rewrite the equation with

x^{\frac{1}{5}} = u

40 - 0.2 u^{5} - 0.006 u^{8} = 0

Solve

40 - 0.2 u^{5} - 0.006 u^{8} = 0 : u \approx 2.64212 \dots, u \approx - 3.55768 \dots

u \approx 2.64212 \dots, u \approx - 3.55768 \dots

Substitute back

u = x^{\frac{1}{5}},

solve for

x

Solve

x^{\frac{1}{5}} = 2.64212 \dots : x = 128.75591 \dots

Solve

x^{\frac{1}{5}} = - 3.55768 \dots : x = - 569.95374 \dots

x = 128.75591 \dots, x = - 569.95374 \dots

Verify Solutions:

x = 128.75591 \dots

True

, x = - 569.95374 \dots

True

The solutions are

x = 128.75591 \dots, x = - 569.95374 \dots

x + 7 + 8 = 4

108 = 0.2 x^{\frac{3}{2}}

x + 2 + 4 = x

2 x + 3 = 1 - x + 1

What is the answer to 40-0.2x-0.006x^{1.6}=0 ?
The answer to 40-0.2x-0.006x^{1.6}=0 is x=128.75591…,x=-569.95374…
Solve for x: 40-0.2x-0.006x^{1.6}=0
The solution is x=128.75591…,x=-569.95374…