What is the answer to (2x+1)^{0.3}=x-4 ?

The answer to (2x+1)^{0.3}=x-4 is x\approx 6.17602…

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(2x+1)^{0.3}=x-4

(2 x + 1)^{0.3} = x - 4

x \approx 6.17602 \dots

Solution steps

(2 x + 1)^{0.3} = x - 4

Take both sides of the equation to the power of

10 : (2 x + 1)^{3} = x^{10} - 40 x^{9} + 720 x^{8} - 7680 x^{7} + 53760 x^{6} - 258048 x^{5} + 860160 x^{4} - 1966080 x^{3} + 2949120 x^{2} - 2621440 x + 1048576

(2 x + 1)^{3} = x^{10} - 40 x^{9} + 720 x^{8} - 7680 x^{7} + 53760 x^{6} - 258048 x^{5} + 860160 x^{4} - 1966080 x^{3} + 2949120 x^{2} - 2621440 x + 1048576

Solve

(2 x + 1)^{3} = x^{10} - 40 x^{9} + 720 x^{8} - 7680 x^{7} + 53760 x^{6} - 258048 x^{5} + 860160 x^{4} - 1966080 x^{3} + 2949120 x^{2} - 2621440 x + 1048576 : x \approx 2.31975 \dots, x \approx 6.17602 \dots

x \approx 2.31975 \dots, x \approx 6.17602 \dots

Verify Solutions:

x \approx 2.31975 \dots

False

, x \approx 6.17602 \dots

True

The solution is

x \approx 6.17602 \dots

x - 1 - x = - 3

3 x + 1 - 2 x - 1 = 4

12 + 4 x = x

8 = 6 x - 2

x = 12 - x

What is the answer to (2x+1)^{0.3}=x-4 ?
The answer to (2x+1)^{0.3}=x-4 is x\approx 6.17602…
Solve for x: (2x+1)^{0.3}=x-4
The solution is x\approx 6.17602…