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

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

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

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

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

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

Solution steps

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

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)}

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

Rewrite the equation with

x^{\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 = 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

1 + 2 + x - 5 = 2

x^{2} - x - 3 = x + 2

x - 8 - 2 x = 0

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