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Popular >

x^9+3x^6+3x^3-16x-7=0

Solution

x^{9} + 3 x^{6} + 3 x^{3} - 16 x - 7 = 0

Solution

x \approx - 0.45339 \dots, x \approx - 1.52403 \dots, x \approx 1.26993 \dots

Solution steps

x^{9} + 3 x^{6} + 3 x^{3} - 16 x - 7 = 0

Find one solution for

x^{9} + 3 x^{6} + 3 x^{3} - 16 x - 7 = 0

using Newton-Raphson:

x \approx - 0.45339 \dots

Apply long division:

\frac{x ^{9} + 3 x ^{6} + 3 x ^{3} - 16 x - 7}{x + 0.45339 \dots} = x^{8} - 0.45339 \dots x^{7} + 0.20556 \dots x^{6} + 2.90679 \dots x^{5} - 1.31793 \dots x^{4} + 0.59754 \dots x^{3} + 2.72907 \dots x^{2} - 1.23735 \dots x - 15.43898 \dots

x^{8} - 0.45339 \dots x^{7} + 0.20556 \dots x^{6} + 2.90679 \dots x^{5} - 1.31793 \dots x^{4} + 0.59754 \dots x^{3} + 2.72907 \dots x^{2} - 1.23735 \dots x - 15.43898 \dots \approx 0

Find one solution for

x^{8} - 0.45339 \dots x^{7} + 0.20556 \dots x^{6} + 2.90679 \dots x^{5} - 1.31793 \dots x^{4} + 0.59754 \dots x^{3} + 2.72907 \dots x^{2} - 1.23735 \dots x - 15.43898 \dots = 0

using Newton-Raphson:

x \approx - 1.52403 \dots

Apply long division:

\frac{x ^{8} - 0.45339 \dots x ^{7} + 0.20556 \dots x ^{6} + 2.90679 \dots x ^{5} - 1.31793 \dots x ^{4} + 0.59754 \dots x ^{3} + 2.72907 \dots x ^{2} - 1.23735 \dots x - 15.43898 \dots}{x + 1.52403 \dots} = x^{7} - 1.97743 \dots x^{6} + 3.21925 \dots x^{5} - 1.99947 \dots x^{4} + 1.72934 \dots x^{3} - 2.03804 \dots x^{2} + 5.83512 \dots x - 10.13031 \dots

x^{7} - 1.97743 \dots x^{6} + 3.21925 \dots x^{5} - 1.99947 \dots x^{4} + 1.72934 \dots x^{3} - 2.03804 \dots x^{2} + 5.83512 \dots x - 10.13031 \dots \approx 0

Find one solution for

x^{7} - 1.97743 \dots x^{6} + 3.21925 \dots x^{5} - 1.99947 \dots x^{4} + 1.72934 \dots x^{3} - 2.03804 \dots x^{2} + 5.83512 \dots x - 10.13031 \dots = 0

using Newton-Raphson:

x \approx 1.26993 \dots

Apply long division:

\frac{x ^{7} - 1.97743 \dots x ^{6} + 3.21925 \dots x ^{5} - 1.99947 \dots x ^{4} + 1.72934 \dots x ^{3} - 2.03804 \dots x ^{2} + 5.83512 \dots x - 10.13031 \dots}{x - 1.26993 \dots} = x^{6} - 0.70749 \dots x^{5} + 2.32077 \dots x^{4} + 0.94776 \dots x^{3} + 2.93294 \dots x^{2} + 1.68661 \dots x + 7.97702 \dots

x^{6} - 0.70749 \dots x^{5} + 2.32077 \dots x^{4} + 0.94776 \dots x^{3} + 2.93294 \dots x^{2} + 1.68661 \dots x + 7.97702 \dots \approx 0

Find one solution for

x^{6} - 0.70749 \dots x^{5} + 2.32077 \dots x^{4} + 0.94776 \dots x^{3} + 2.93294 \dots x^{2} + 1.68661 \dots x + 7.97702 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.45339 \dots, x \approx - 1.52403 \dots, x \approx 1.26993 \dots

Popular Examples

x^3-3x^2-9x+11=0

x^{3} - 3 x^{2} - 9 x + 11 = 0

x x^{2} + 6 x + 8 = 0

x^{3} - 28 = 100

x^{4} - 8 x^{2} + 1 = 0

solvefor x,y+7=3x^3 solve for

x, y + 7 = 3 x^{3}