What are the solutions to the equation 5x^{16}=10x+15 ?

The solutions to the equation 5x^{16}=10x+15 are x=-1,x\approx 1.10877…

Find the zeros of 5x^{16}=10x+15

The zeros of 5x^{16}=10x+15 are x=-1,x\approx 1.10877…

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5 x^{16} = 10 x + 15

x = - 1, x \approx 1.10877 \dots

Solution steps

5 x^{16} = 10 x + 15

Move

15

to the left side

5 x^{16} - 15 = 10 x

Move

10 x

to the left side

5 x^{16} - 15 - 10 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

5 x^{16} - 10 x - 15 = 0

Factor

5 x^{16} - 10 x - 15 : 5 (x + 1) (x^{15} - x^{14} + x^{13} - x^{12} + x^{11} - x^{10} + x^{9} - x^{8} + x^{7} - x^{6} + x^{5} - x^{4} + x^{3} - x^{2} + x - 3)

5 (x + 1) (x^{15} - x^{14} + x^{13} - x^{12} + x^{11} - x^{10} + x^{9} - x^{8} + x^{7} - x^{6} + x^{5} - x^{4} + x^{3} - x^{2} + x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x^{15} - x^{14} + x^{13} - x^{12} + x^{11} - x^{10} + x^{9} - x^{8} + x^{7} - x^{6} + x^{5} - x^{4} + x^{3} - x^{2} + x - 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x^{15} - x^{14} + x^{13} - x^{12} + x^{11} - x^{10} + x^{9} - x^{8} + x^{7} - x^{6} + x^{5} - x^{4} + x^{3} - x^{2} + x - 3 = 0 : x \approx 1.10877 \dots

The solutions are

x = - 1, x \approx 1.10877 \dots

21 x^{4} = 119 x^{2} - 1

(x^{2} - 1) (x^{2} - 4) = 0

9 x^{3} = x

x = \frac{4}{3} π r^{3}, r

3 x^{3} + 15 = 207

What are the solutions to the equation 5x^{16}=10x+15 ?
The solutions to the equation 5x^{16}=10x+15 are x=-1,x\approx 1.10877…
Find the zeros of 5x^{16}=10x+15
The zeros of 5x^{16}=10x+15 are x=-1,x\approx 1.10877…