What is the answer to 20+0.6N=60+0.4N-0.006N^{1.6} ?

The answer to 20+0.6N=60+0.4N-0.006N^{1.6} is N=128.75591…,N=-569.95374…

Solve for N: 20+0.6N=60+0.4N-0.006N^{1.6}

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

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20 + 0.6 N = 60 + 0.4 N - 0.006 N^{1.6}

N = 128.75591 \dots, N = - 569.95374 \dots

Solution steps

20 + 0.6 N = 60 + 0.4 N - 0.006 N^{1.6}

Use the following exponent property

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

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

20 + 0.6 (N^{\frac{1}{5}})^{5} = 60 + 0.4 (N^{\frac{1}{5}})^{5} - 0.006 (N^{\frac{1}{5}})^{8}

Rewrite the equation with

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

20 + 0.6 u^{5} = 60 + 0.4 u^{5} - 0.006 u^{8}

Solve

20 + 0.6 u^{5} = 60 + 0.4 u^{5} - 0.006 u^{8} : u \approx 2.64212 \dots, u \approx - 3.55768 \dots

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

Substitute back

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

solve for

N

Solve

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

Solve

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

N = 128.75591 \dots, N = - 569.95374 \dots

Verify Solutions:

N = 128.75591 \dots

True

, N = - 569.95374 \dots

True

The solutions are

N = 128.75591 \dots, N = - 569.95374 \dots

(3 x + 1)^{\frac{1}{4}} + 5 = 3

2 x + 5 x - 6 = 4

5 x^{2} - 44 = 3 x - 8

x - 4 x - 2 = 0

What is the answer to 20+0.6N=60+0.4N-0.006N^{1.6} ?
The answer to 20+0.6N=60+0.4N-0.006N^{1.6} is N=128.75591…,N=-569.95374…
Solve for N: 20+0.6N=60+0.4N-0.006N^{1.6}
The solution is N=128.75591…,N=-569.95374…