What are the solutions to the equation (x-2)^3-x^3+6x+7=0 ?

The solutions to the equation (x-2)^3-x^3+6x+7=0 are x=(9-5sqrt(3))/6 ,x=(9+5sqrt(3))/6

Find the zeros of (x-2)^3-x^3+6x+7=0

The zeros of (x-2)^3-x^3+6x+7=0 are x=(9-5sqrt(3))/6 ,x=(9+5sqrt(3))/6

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(x - 2)^{3} - x^{3} + 6 x + 7 = 0

x = \frac{9 - 5 3}{6}, x = \frac{9 + 5 3}{6}

Decimal Notation

x = 0.05662 \dots, x = 2.94337 \dots

Solution steps

(x - 2)^{3} - x^{3} + 6 x + 7 = 0

Expand

(x - 2)^{3} - x^{3} + 6 x + 7 : - 6 x^{2} + 18 x - 1

- 6 x^{2} + 18 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 18 \pm 1 8 ^{2} - 4 ( - 6 ) ( - 1 )}{2 ( - 6 )}

1 8^{2} - 4 (- 6) (- 1) = 103

x_{1, 2} = \frac{- 18 \pm 10 3}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 18 + 10 3}{2 ( - 6 )}, x_{2} = \frac{- 18 - 10 3}{2 ( - 6 )}

x = \frac{- 18 + 10 3}{2 ( - 6 )} : \frac{9 - 5 3}{6}

x = \frac{- 18 - 10 3}{2 ( - 6 )} : \frac{9 + 5 3}{6}

The solutions to the quadratic equation are:

x = \frac{9 - 5 3}{6}, x = \frac{9 + 5 3}{6}

x, x^{2} + y^{2} + z^{2} - 2 x + 4 y + 5 = 0

15 x^{2} + 15 = 34 x

(a + b)^{2} x^{2} + 8 (a^{2} - b^{2}) x + 16 (a - b)^{2} = 0

5 x (3 x + 2 x) - 3 x = 40

x, (p - 3) \cdot x^{2} - 2 (p - 3) x + 2 = 0

What are the solutions to the equation (x-2)^3-x^3+6x+7=0 ?
The solutions to the equation (x-2)^3-x^3+6x+7=0 are x=(9-5sqrt(3))/6 ,x=(9+5sqrt(3))/6
Find the zeros of (x-2)^3-x^3+6x+7=0
The zeros of (x-2)^3-x^3+6x+7=0 are x=(9-5sqrt(3))/6 ,x=(9+5sqrt(3))/6