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Popular >

-(x-3)(x+5)x^2+x-8=x-3x

Solution

- (x - 3) (x + 5) x^{2} + x - 8 = x - 3 x

Solution

x \approx 3.01432 \dots, x \approx 0.67309 \dots, x \approx - 0.80809 \dots, x \approx - 4.87932 \dots

Solution steps

- (x - 3) (x + 5) x^{2} + x - 8 = x - 3 x

Expand

- (x - 3) (x + 5) x^{2} + x - 8 : - x^{4} - 2 x^{3} + 15 x^{2} + x - 8

- x^{4} - 2 x^{3} + 15 x^{2} + x - 8 = - 2 x

Move

2 x

to the left side

- x^{4} - 2 x^{3} + 15 x^{2} + 3 x - 8 = 0

Find one solution for

- x^{4} - 2 x^{3} + 15 x^{2} + 3 x - 8 = 0

using Newton-Raphson:

x \approx 3.01432 \dots

Apply long division:

\frac{- x ^{4} - 2 x ^{3} + 15 x ^{2} + 3 x - 8}{x - 3.01432 \dots} = - x^{3} - 5.01432 \dots x^{2} - 0.11478 \dots x + 2.65399 \dots

- x^{3} - 5.01432 \dots x^{2} - 0.11478 \dots x + 2.65399 \dots \approx 0

Find one solution for

- x^{3} - 5.01432 \dots x^{2} - 0.11478 \dots x + 2.65399 \dots = 0

using Newton-Raphson:

x \approx 0.67309 \dots

Apply long division:

\frac{- x ^{3} - 5.01432 \dots x ^{2} - 0.11478 \dots x + 2.65399 \dots}{x - 0.67309 \dots} = - x^{2} - 5.68741 \dots x - 3.94296 \dots

- x^{2} - 5.68741 \dots x - 3.94296 \dots \approx 0

Find one solution for

- x^{2} - 5.68741 \dots x - 3.94296 \dots = 0

using Newton-Raphson:

x \approx - 0.80809 \dots

Apply long division:

\frac{- x ^{2} - 5.68741 \dots x - 3.94296 \dots}{x + 0.80809 \dots} = - x - 4.87932 \dots

- x - 4.87932 \dots \approx 0

x \approx - 4.87932 \dots

The solutions are

x \approx 3.01432 \dots, x \approx 0.67309 \dots, x \approx - 0.80809 \dots, x \approx - 4.87932 \dots

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