What are the solutions to the equation 25b^2+35b^4=45b^5 ?

The solutions to the equation 25b^2+35b^4=45b^5 are b=0,b\approx 1.17807…

Find the zeros of 25b^2+35b^4=45b^5

The zeros of 25b^2+35b^4=45b^5 are b=0,b\approx 1.17807…

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25 b^{2} + 35 b^{4} = 45 b^{5}

b = 0, b \approx 1.17807 \dots

Solution steps

25 b^{2} + 35 b^{4} = 45 b^{5}

Switch sides

45 b^{5} = 25 b^{2} + 35 b^{4}

Move

35 b^{4}

to the left side

45 b^{5} - 35 b^{4} = 25 b^{2}

Move

25 b^{2}

to the left side

45 b^{5} - 35 b^{4} - 25 b^{2} = 0

Factor

45 b^{5} - 35 b^{4} - 25 b^{2} : 5 b^{2} (9 b^{3} - 7 b^{2} - 5)

5 b^{2} (9 b^{3} - 7 b^{2} - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

b = 0 or 9 b^{3} - 7 b^{2} - 5 = 0

Solve

9 b^{3} - 7 b^{2} - 5 = 0 : b \approx 1.17807 \dots

The solutions are

b = 0, b \approx 1.17807 \dots

12 x^{3} + 13 x^{2} + x = 0

2 x^{3} - 5 x^{2} + 6 x + 27 = 0

2 x^{3} + 7 x^{2} + 7 x + 2 = 0

3 c^{3} + 21 c^{2} - 54 c = 0

- 3 m^{4} = 48 m^{2}

What are the solutions to the equation 25b^2+35b^4=45b^5 ?
The solutions to the equation 25b^2+35b^4=45b^5 are b=0,b\approx 1.17807…
Find the zeros of 25b^2+35b^4=45b^5
The zeros of 25b^2+35b^4=45b^5 are b=0,b\approx 1.17807…