What are the solutions to the equation (x-2)^3-(x-3)^3=33 ?

The solutions to the equation (x-2)^3-(x-3)^3=33 are x=(15+sqrt(393))/6 ,x=(15-sqrt(393))/6

Find the zeros of (x-2)^3-(x-3)^3=33

The zeros of (x-2)^3-(x-3)^3=33 are x=(15+sqrt(393))/6 ,x=(15-sqrt(393))/6

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(x - 2)^{3} - (x - 3)^{3} = 33

x = \frac{15 + 393}{6}, x = \frac{15 - 393}{6}

Decimal Notation

x = 5.80403 \dots, x = - 0.80403 \dots

Solution steps

(x - 2)^{3} - (x - 3)^{3} = 33

Expand

(x - 2)^{3} - (x - 3)^{3} : 3 x^{2} - 15 x + 19

3 x^{2} - 15 x + 19 = 33

Move

33

to the left side

3 x^{2} - 15 x - 14 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 15 ) \pm ( - 15 ) ^{2} - 4 \cdot 3 ( - 14 )}{2 \cdot 3}

(- 15)^{2} - 4 \cdot 3 (- 14) = 393

x_{1, 2} = \frac{- ( - 15 ) \pm 393}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 15 ) + 393}{2 \cdot 3}, x_{2} = \frac{- ( - 15 ) - 393}{2 \cdot 3}

x = \frac{- ( - 15 ) + 393}{2 \cdot 3} : \frac{15 + 393}{6}

x = \frac{- ( - 15 ) - 393}{2 \cdot 3} : \frac{15 - 393}{6}

The solutions to the quadratic equation are:

x = \frac{15 + 393}{6}, x = \frac{15 - 393}{6}

x^{2} - 10 x - 10 = 10

s^{2} + 4 s + 50 = 0

\frac{1}{10} x (10 - x) - 1 = 0

m^{2} + 14 m = 120

s^{2} - 16 = 0

What are the solutions to the equation (x-2)^3-(x-3)^3=33 ?
The solutions to the equation (x-2)^3-(x-3)^3=33 are x=(15+sqrt(393))/6 ,x=(15-sqrt(393))/6
Find the zeros of (x-2)^3-(x-3)^3=33
The zeros of (x-2)^3-(x-3)^3=33 are x=(15+sqrt(393))/6 ,x=(15-sqrt(393))/6