What are the solutions to the equation (x-3)^3=x^3-63 ?

The solutions to the equation (x-3)^3=x^3-63 are x=-1,x=4

Find the zeros of (x-3)^3=x^3-63

The zeros of (x-3)^3=x^3-63 are x=-1,x=4

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(x - 3)^{3} = x^{3} - 63

x = - 1, x = 4

Solution steps

(x - 3)^{3} = x^{3} - 63

Expand

(x - 3)^{3} : x^{3} - 9 x^{2} + 27 x - 27

x^{3} - 9 x^{2} + 27 x - 27 = x^{3} - 63

Move

63

to the left side

x^{3} - 9 x^{2} + 27 x + 36 = x^{3}

Move

x^{3}

to the left side

- 9 x^{2} + 27 x + 36 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 27 \pm 2 7 ^{2} - 4 ( - 9 ) \cdot 36}{2 ( - 9 )}

2 7^{2} - 4 (- 9) \cdot 36 = 45

x_{1, 2} = \frac{- 27 \pm 45}{2 ( - 9 )}

Separate the solutions

x_{1} = \frac{- 27 + 45}{2 ( - 9 )}, x_{2} = \frac{- 27 - 45}{2 ( - 9 )}

x = \frac{- 27 + 45}{2 ( - 9 )} : - 1

x = \frac{- 27 - 45}{2 ( - 9 )} : 4

The solutions to the quadratic equation are:

x = - 1, x = 4

x^{2} + 16 x = 7

m^{2} - 4 m = 5

- 2 x^{2} - 7 x - 1 = 0

3 x^{2} + 2 x - 6

s^{2} = 25

What are the solutions to the equation (x-3)^3=x^3-63 ?
The solutions to the equation (x-3)^3=x^3-63 are x=-1,x=4
Find the zeros of (x-3)^3=x^3-63
The zeros of (x-3)^3=x^3-63 are x=-1,x=4