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Popular >

(x+3)^2-(3x-1)^2=x^3+4

Solution

(x + 3)^{2} - (3 x - 1)^{2} = x^{3} + 4

Solution

x \approx - 0.28213 \dots, x \approx 1.53262 \dots, x \approx - 9.25048 \dots

Solution steps

(x + 3)^{2} - (3 x - 1)^{2} = x^{3} + 4

Expand

(x + 3)^{2} - (3 x - 1)^{2} : - 8 x^{2} + 12 x + 8

- 8 x^{2} + 12 x + 8 = x^{3} + 4

Switch sides

x^{3} + 4 = - 8 x^{2} + 12 x + 8

Move

8

to the left side

x^{3} - 4 = - 8 x^{2} + 12 x

Move

12 x

to the left side

x^{3} - 4 - 12 x = - 8 x^{2}

Move

8 x^{2}

to the left side

x^{3} - 4 - 12 x + 8 x^{2} = 0

Write in the standard form

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

x^{3} + 8 x^{2} - 12 x - 4 = 0

Find one solution for

x^{3} + 8 x^{2} - 12 x - 4 = 0

using Newton-Raphson:

x \approx - 0.28213 \dots

Apply long division:

\frac{x ^{3} + 8 x ^{2} - 12 x - 4}{x + 0.28213 \dots} = x^{2} + 7.71786 \dots x - 14.17749 \dots

x^{2} + 7.71786 \dots x - 14.17749 \dots \approx 0

Find one solution for

x^{2} + 7.71786 \dots x - 14.17749 \dots = 0

using Newton-Raphson:

x \approx 1.53262 \dots

Apply long division:

\frac{x ^{2} + 7.71786 \dots x - 14.17749 \dots}{x - 1.53262 \dots} = x + 9.25048 \dots

x + 9.25048 \dots \approx 0

x \approx - 9.25048 \dots

The solutions are

x \approx - 0.28213 \dots, x \approx 1.53262 \dots, x \approx - 9.25048 \dots

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